Question

1. You are given the graph of a function f. Determine the intervals where f is increasing, constant, or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

The x y-coordinate plane is given. The curve enters the window in the second quadrant, goes down and right becoming less steep, changes direction at the point (−1, 0), goes up and right becoming more steep, passes through the approximate point (−0.58, 0.44), goes up and right becoming less steep, changes direction at the point (0, 1), goes down and right becoming more steep, passes through the approximate point (0.58, 0.44), goes down and right becoming less steep, changes direction at the point (1, 0), goes up and right becoming more steep, and exits the window in the first quadrant.

increasing=

constant=

decreasing=

2.Solar Panel Power Output

The graph of the function f shown in the accompanying figure gives the average "fixed" solar panel power output over a 15-hr period on a typical day. Determine the interval(s) where f is increasing, the interval(s) where f is constant, and the interval(s) where f is decreasing. Here,

t = 0

corresponds to 5 a.m. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

The t y-coordinate plane is given. The t-axis is labeled: (hr) and the y-axis is labeled: Solar panel operating capacity (%).

• The curve begins above the t value 0, goes up and right until it reaches the t value 6 and approximate y value of 100.
• The curve continues from the t value 6 horizontally right until it reaches the t value 9.
• The curve continues from the t value 9 going down and right until it reaches the t value 14 and approximate y value of 5.
• The curve continues from the t value 14 horizontally right until it reaches the t value 15.

Source: Solarcity.com/California

increasing=

constant=

decreasing=

3.You are given the graph of a function f. Determine the relative maxima and relative minima, if any. (If an answer does not exist, enter DNE.)

The x y-coordinate plane is given. The function enters the window in the second quadrant, goes down and right, changes direction at the point (−4, 0), goes up and right becoming less steep, changes direction at the point (0, 16), goes down and right becoming more steep, changes direction at the point (4, 0), goes up and right, and exits the window in the first quadrant.

relative minimumsmaller x-value

(x, y)

=

relative minimumlarger x-value

(x, y)

=

(x, y)relative maximum

=

4.You are given the graph of a function f. Determine the relative maxima and relative minima, if any. (If an answer does not exist, enter DNE.)

The x y-coordinate plane is given. The curve with 3 parts enters the window at in the second quadrant, goes down and right becoming more steep, exits in the third quadrant almost vertically just to the left of x = −2, reenters in the second quadrant almost vertically just to the right of x = −2, goes down and right becoming less steep, changes direction at the point (0, 4), goes up and right becoming more steep, exits almost vertically just to the left of x = 2, reenters in the fourth quadrant almost vertically just to the right of x = 2, goes up and right becoming less steep, and exits the window in the first quadrant.

relative minimum

(x, y)

=

  (x, y)relative maximum

=

5.Find the x-value(s) of the relative maxima and relative minima, if any, of the function. (If an answer does not exist, enter DNE.)

f(x) = 1/2x² − 4x + 1
relative maxima:

x =

relative minima:

x =

6.Find the relative maxima and relative minima, if any, of the function. (If an answer does not exist, enter DNE.)

f(x) = x³ − 12x + 10

relative maximum(x, y)=

relative minimum(x, y)=

7.Find the relative maxima and relative minima, if any, of the function. (If an answer does not exist, enter DNE.)

F(t) = 3t⁵ − 5t³ + 12

relative maximum(x, y)=

relative minimum(x, y)=

8.Find the relative maxima and relative minima, if any, of the function. (If an answer does not exist, enter DNE.)

f(x) = X/X+4

relative minimum (x, y)=

relative maximum(x, y)=

9.

You are given the graph of a function f.

The x y-coordinate plane is given. A curve and 2 vertical lines are graphed.

• A vertical line crosses the x-axis at x = −4.
• A vertical line crosses the x-axis at x = 4.
• The curve with 3 parts enters the window just above the x−axis, goes up and right becoming more steep, exits almost vertically just to the left of x = −4, reenters almost vertically just to the right of x = −4, goes up and right becoming less steep, changes direction at the point (0, −0.5), goes down and right becoming more steep, exits almost vertically just to the left of x = 4, reenters almost vertically just to the right of x = 4, goes down and right becoming less steep, and exits the window just above the x−axis.

Determine the intervals where the graph of f is concave upward and where it is concave downward. (Enter your answers using interval notation.)

concave upward=

concave downward=

Find the inflection point of f, if any. (If an answer does not exist, enter DNE.)

(x, y) =

10.

You are given the graph of a function f.

The x y-coordinate plane is given. The curve enters the window in the second quadrant nearly horizontal, goes down and right becoming more steep, is nearly vertical at the point (0, 1), goes down and right becoming less steep, crosses the x-axis at approximately x = 1, and exits the window just below the x−axis.

Determine the intervals where the graph of f is concave upward and where it is concave downward. (Enter your answers using interval notation.)

concave upward=

concave downward=

Find the inflection point of f. (If an answer does not exist, enter DNE.)

(x, y) =

11.

Refer to the graph of f shown in the following figure.

The x y-coordinate plane is given. There is 1 curve and 9 dashed lines on the graph.

• The curve starts at the point (0, 1), goes up and right becoming more steep, passes through the approximate point (2, 2.4), goes up and right becoming less steep, changes direction at the approximate point (3, 3), goes down and right becoming more steep, passes through the approximate point (4, 2.2), goes down and right becoming less steep, changes direction at the point (5, 1), goes up and right becoming more steep, passes through the point (6, 2), goes up and right becoming almost horizontal at the point (7, 3), goes up and right becoming more steep, changes direction at the point (9, 6), goes down and right becoming less steep, and exits the window at the point (12, 2).
• The 9 dashed vertical lines extend from the x−axis to the curve at x = 1, 2, 3, 4, 5, 6, 7, 9, and 12.

(a)

Find the intervals where f is concave upward and the intervals where f is concave downward. (Enter your answers using interval notation.)

concave upward=

concave downward=

(b)

Find the inflection points of f. (Order your answers from smallest to largest x, then from smallest to largest y. If an answer does not exist, enter DNE.)

(x, y)	=
(x, y)	=
(x, y)	=
(x, y)	=

12.

Determine where the function is concave upward and where it is concave downward. (Enter your answer using interval notation. If an answer does not exist, enter DNE.)

g(x) = −x² + 9x + 8

concave upward=

concave downward=

13.

Determine where the function is concave upward and where it is concave downward. (Enter your answer using interval notation. If an answer does not exist, enter DNE.)

g(x) =

x − 4

concave upward=

concave downward=

14.

Determine where the function is concave upward and where it is concave downward. (Enter your answer using interval notation. If an answer does not exist, enter DNE.)

g(x) =

x

x + 8

concave upward=

concave downward=

15.

Determine where the function is concave upward and where it is concave downward. (Enter your answer using interval notation. If an answer does not exist, enter DNE.)

f(x) =

x + 3

x − 3

concave upward=

concave downward=

16.

Determine where the function is concave upward and where it is concave downward. (Enter your answer using interval notation. If an answer does not exist, enter DNE.)

f(x) = (x − 3)^2/3

concave upward=

concave downward=

17.

Find the inflection point(s), if any, of the function. (If an answer does not exist, enter DNE.)

g(x) = 4x⁴ − 8x³ + 1

smaller x-value (x, y)	=
larger x-value (x, y)	=

18.

Find the inflection point, if any, of the function. (If an answer does not exist, enter DNE.)

f(x) = (x − 8)^4/3

(x, y) =

19. Find the inflection point, if any, of the function. (If an answer does not exist, enter DNE.) f(x) = 6 + 6 x (x, y) = 20.

Answer 1