a) The critical values are x = For your answers for b & c, (enter your values separated by a comma) • enter your interval(s) as "(a, b)" ● if you have more than one interval, separate them with a comma. (1, 3), (7, 00) etc. • Use "-oo" or "oo" for - ∞ or ∞ b) The function is increasing on interval(s): c) The function is decreasing on interval(s):

Q: Differentiate the function.

A:

Q: f(x) = 5x csc x 7 f (x) = 100 + 2cosx – 3x+x 3.

A: *formula:- d/dx (cscx) = -cscx*cotx. d/dx (x^{n}) = nx^{n-1}. d/dx (cosx) = -sinx.

Q: for question d in the first line, why is the derivative of u(x) 1/x^2 and not 2/x?

A:

Q: Compute the derivative of y= [(x+1)/x^3-1)]^1/2

A: The given function is y=x+1x3-112. Obtain the derivative as follows.

Q: ļim (* +4)- ƒ(x) 3. Find the derivative of the following functions using the Show all your steps. a.…

A: f'(x)=lim(h tends to 0) {f(x+h)-f(x)}/h use this for derivative

Q: Find the derivative of ?(?) = 6 sec2(7x? − 3).

A: Follow the procedure given below.

Q: Consider the function f(x)= x^2−3x.   Compute the derivative using the definition

A: In order to solve this question we will use the concept of first principle which defines derivative.

Q: Find the f derivative of x given f(x)=(3x)^-1

A: Calculation:Compute the derivative of f(x) = (3x)−1 as follows.

Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A: f'(x)=-2x8-x2;(2,8)