Finding the stationary points of a given function

Question

If given f(x) = x³e^x,

a) How can I find coordinates of the stationary point(s) of f(x)

b) How can I determine the nature of the stationary point of f(x).

c) On what interval is the function f(x) increasing?

Answer 1

Greetings,

To find the stationary points (which is a term I normally don’t use) take the derivative and set it equal to zero.

You will end up with an equation that factors. If you can then determine x you can find y=f(x).

To determine the nature of the stationary point look at the value of the derivative before and after passing through. If the derivative goes from positive to negative you have a relative maximum (slope goes from positive to negative). If the derivative goes from negative to positive you have a relative min. As for when the function is increasing think about what the derivative represents. You can then set up an inequality.

Answer 2

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