find all critical points and global extremes of each function on the given intervals on the entire number line.

a)f(x) = 2 - x^3

b) f(x)= x-e^x

c)f(x) = 2x^3 - 96x + 42 (Local min and max only)

Use the Second Derivative Test to determine whether each point (x, f(x)) is a local maximum, a local minimum or neither

a) f(x)=2x^3-15x^2+6, X=0,5

b) h(x)=x^4-8x^2-2, X=-2,0,2

use information from the derivatives of each function to help you graph the function. Find all local maximums and minimums of each function.

a)f(x) = x^3 - 3x^2 - 9x - 5

b) h(x) = x^4 - 8x^2 + 3