For the followings problems, consider a function that is twice differentiable. This means that his differentiable and its derivative, h', is also differentiable. Some values of h'(x) are given in the table below: x -8-6-4-2 0 24 6 8 h'(x) 3 7 0 -3 -5 -4 0 -2 6 Determine all intervals in which h must have an inflection point. (-8,-4) (-4,0) (0,4) (2,6) (4,8)

Use the constant, power, or constant multiple rule, whichever is applicable, to find the derivative of the following functions. with solution please.

The following problems involve f(x) = 3x4 -8x³ - 66x² + 144x + 400 1. Find the relative extrema of this function using the Second Derivative Test. Discuss the behavior of the function (increase/decrease) and how it relates to f'(x). 2. Use the information from problem 1 to find the possible inflection points. Discuss the concavity, and how it relates to f'(x).

consider the product of 3 functions w= f x g x h. Find an expression for the derivative of the product in terms of the three given functions and their derivatives. (Remeber that the product of three numbers can be thought of as the product of two of them with the third  w'=