Consider the function on the interval (0, 2π). f(x) = sin(x)/ 2
+ (cos(x))^2 (a) Find the open intervals on which the function is
increasing or decreasing. (Enter your answers using interval
notation.) increasing decreasing (b) Apply the First Derivative
Test to identify the relative extrema. relative maximum (x, y) =
relative minimum (x, y) =
Consider the function on the interval (0, 2π).
f(x) = sin(x) cos(x) + 2
(a) Find the open interval(s) on which the function is
increasing or decreasing. (Enter your answers using interval
notation.)
increasing
( )
decreasing
( )
(b) Apply the First Derivative Test to identify all relative
extrema.
relative maxima
(x, y) =
(smaller x-value)
(x, y) =
( )
(larger x-value)
relative minima
(x, y) =
(smaller x-value)
(x, y) =
...
Find f
1)f”(x)=-2+12x-12x(Square), f’(0)=12
F(x)=?
2)Find a function f such that f’(x)=5x cube and the line
5x+y=0 is the tangent to the graph of f
F(x)=?
3)A particle is moving with the given data. Find the position
of the particle
a(t)=11sin(t)+4cos(t), s(0)=0, s(2pi)=16
s(t)=?
(please i need help)
Expand the function, f(x) = x, defined over the interval 0 <x
<2, in terms of:
A Fourier sine series, using an odd extension of f(x)
and A Fourier cosine series, using an even extension of f(x)
Let f(x, y) be a function such that f(0, 0) = 1, f(0, 1) = 2,
f(1, 0) = 3, f(1, 1) = 5, f(2, 0) = 5, f(2, 1) = 10. Determine the
Lagrange interpolation F(x, y) that interpolates the above data.
Use Lagrangian bi-variate interpolation to solve this and also show
the working steps.
9. Given the function: f(x)=3x2+5x-17
a. find the interval where the function is increasing and where
it is decreasing.
b. Clearly state the critical number(s) of the function.
c. Find the relative extrema of the function( using 1st
derivative test). answer should be in (x,y)
10. Given the function: x3 - x2 + 52x -
17
a. determine the intervals where the graph of the given function
is concave upward and where it is concave downward.
b. Find any inflection...
The average value of a function f over the interval [-2,3] is
-6, and the average value of f over the interval [3,5] is 20. What
is the average value of f over the interval [-2,5]?
1.
Find the critical numbers of the function f (x) = x^3− 12x in the
interval [0, 3]. Then find the absolute maximum and the absolute
minimum of f(x) on the interval [0,3].
2. Using only the limit definition of derivative, find the
derivative of f(x) = x^2− 6x (do not use the formulas of
derivatives).