# First derivative stationary point problem

• Sep 10th 2008, 08:15 AM
offahengaway and chips
First derivative stationary point problem
Hi there, I am getting a little bit stuck on a calculus question,

I am required to find the stationary points of g(x) = e^x/7 / sqrt (10 + x^2).

from this I need to use the first derivative test to classify each stationary point as a maximum or minimum.

Many thanks
• Sep 10th 2008, 01:37 PM
mr fantastic
Quote:

Originally Posted by offahengaway and chips
Hi there, I am getting a little bit stuck on a calculus question,

I am required to find the stationary points of g(x) = e^x/7 / sqrt (10 + x^2).

from this I need to use the first derivative test to classify each stationary point as a maximum or minimum.

Many thanks

Where are you stuck?

Can you get g'(x)?

Can you solve g'(x) = 0?

Can you test nature of the solutions to g'(x) = 0?
• Sep 10th 2008, 10:43 PM
CaptainBlack
Quote:

Originally Posted by offahengaway and chips
Hi there, I am getting a little bit stuck on a calculus question,

I am required to find the stationary points of g(x) = e^x/7 / sqrt (10 + x^2).

from this I need to use the first derivative test to classify each stationary point as a maximum or minimum.

Many thanks

You need to differentiate g(x) to get g'(x), then the stationary points are solutions of the equation g'(x)=0.

A maximum corresponds to a stationary point where the second derivative g''(x) is negative, and a mininmum to a stationary point where the second derivative is positive.

(It's the second derivative test)

RonL