What are the maximum and minimum values of f(x) = x^2 e ^x + 4xe^x + 16?

Question

1. Let f(x) = x 2 e x + 4xex + 16. (a) Determine the maximum and minimum values of f(x) and determine whether they are local or global max/mins. It may help to know that limx→∞ f(x) = ∞ and lim x→−∞ f(x) = 16 (b) Determine the points of inflection and intervals of concavity of f(x). (c) Using your answers to 1a,1b, sketch f(x).

Answer 1

Here is the link to the Desmos graph depicted in the video. The Desmos graph also has rows for first and second derivative which you can enable to determine when those functions are equal to zero.

https://www.desmos.com/calculator/qsosqxt37m