(a) For f(x) = 1 4 x 4 − 6x 2 find the intervals where f(x)...

(a) For f(x) = 1 4 x 4 − 6x 2 find the intervals where f(x) is concave up, and the intervals where f(x) is concave down, and the inflection points of f(x) by the following steps:

i. Compute f 0 (x) and f 00(x).

ii. Show that f 00(x) is equal to 0 only at x = −2 and x = 2.

iii. Observe that f 00(x) is a continuous since it is a polynomial. Conclude that f 00(x) is either always positive or always negative on each of the intervals (−∞, −2), (−2, 2), and (2, ∞).

iv. Evaluate f 00(c) at one point c in each of these three intervals to see if f 00(c) > 0 or f 00(c) < 0, and use this computation to indicate where f(x) is concave up and where f(x) is concave down.

v. Indicate the inflection points (c, f(c)) where f 00(x) changes sign at x = c.

(b) For g(x) = 5 6 x 3 − 1 12x 4 find the intervals where g(x) is concave up, and the intervals where g(x) is concave down, and all inflection points of g(x). HINT: Use same steps as previous problem

Expert Solution

milcah answered 2 years ago

find all intervals on which f(x)=x^3+6x^2+9x+1 is decreasing

Given: f (x) = (x − 2)/(x^2 − x +1)^2 a) Find the intervals where f(x)...

Given: f (x) = (x − 2)/(x^2 − x +1)^2 a) Find the intervals where f(x) is increasing, and decreasing b) Find the intervals where f(x) is concave up, and concave down c) Find the x-coordinate of all inflection points.

Find f. f ''(x) = 4 + 6x + 24x2, f(0) = 4, f (1) = 12

Suppose f is defined by f(x)=3x/(4+x^2), −1≤x<3. What is the domain of f? Find the intervals...

Suppose f is defined by f(x)=3x/(4+x^2), −1≤x<3. What is the domain of f? Find the intervals where f is positive and where f is negative. Does f have any horizontal or vertical asymptotes. If so, find them, and show your supporting calculations. If not, briefly explain why not. Compute f′ and use it to determine the intervals where f is increasing and the intervals where f is decreasing. Find the coordinates of the local extrema of f Make a rough...

part 1) Let f(x) = x^4 − 2x^2 + 3. Find the intervals of concavity of...

part 1) Let f(x) = x^4 − 2x^2 + 3. Find the intervals of concavity of f and determine its inflection point(s). part 2) Find the absolute extrema of f(x) = x^4 + 4x^3 − 8x^2 + 3 on [−1, 2].

Given f(x) = x^4 - 4x^3 1) find the intervals on which f is increasing or...

Given f(x) = x^4 - 4x^3 1) find the intervals on which f is increasing or decreasing. 2) find the local maximum and minimum values of f. 3) find the intervals of concavity and the inflection points

Using extended euclidean algorithm find f(x) and g(x) in: f(x)(x^5 + 4x^4 + 6x^3 + x^2...

Using extended euclidean algorithm find f(x) and g(x) in: f(x)(x^5 + 4x^4 + 6x^3 + x^2 + 4x + 6) + g(x)(x^5 + 5x^4 + 10x^3 + x^2 + 5x + 10) = x^3+1

1) Find the intervals of increasing and decreasing for f(x) = 2x3 – 4x2. 2) Find...

1) Find the intervals of increasing and decreasing for f(x) = 2x3 – 4x2. 2) Find the local minimum and maximum points, if any, of f(x) = 2x3 – 15x2 + 36x – 14. 3) Find the inflection points, if any, of f(x) = 2x3 – 15x2 + 36x – 14. Give the intervals of concavity upward and downward for f(x). 4) Find the absolute maximum and minimum of f(x)= 2x3 – 15x2 + 36x – 14 on the interval...

Find the intervals where the graph of f(x)=2x^4-3x^2 is increasing, decreasing, concave up and concave down....

Find the intervals where the graph of f(x)=2x^4-3x^2 is increasing, decreasing, concave up and concave down. Find any inflection points, local maxima, or local minima. If none exist, write NONE. You must do number line sign charts to receive any credit.

For the function f(x) = x^2 +3x / 2x^2 + 6x +3 find the following, and...

For the function f(x) = x^2 +3x / 2x^2 + 6x +3 find the following, and use it to graph the function. Find: a)(2pts) Domain b)(2pts) Intercepts c)(2pts) Symmetry d) (2pts) Asymptotes e)(4pts) Intervals of Increase or decrease f) (2pts) Local maximum and local minimum values g)(4pts) Concavity and Points of inflection and h)(2pts) Sketch the curve

Question