Problem 1)

Given that for a function

y=f(x)

you are told that

f(x)=3x2ex12ex

a) Find the critical points.

b) Identify the intervals where

y=f(x)

is increasing or decreasing.

c) Use the first derivative test to identify the location of any relative maxima or minima.

Problem 2:Given that \f(x)= x^3+9x^2-18x-2\]

a) find the critical numbers for

y=f(x)

. You mayapproximate these correct to 1 decimal digit.

b) explicitly use a second derivative test to identify the locations of any relative maxima and minima.

c) If there is an inflection point, find both its x and y value, and justify your conclusion about the existence of the inflection point. If there is none, explain why not.