Question

What is the relative maximum value of g(x) for the function shown below?
g(x) = 7 / (x^2 + 5)

Answer 1

Using my current knowledge, wouldn't the relative maximum value be 7/5?

Answer 2

Yup.

Answer 3

Long story short - yup.

Answer 4

Hahaha thanks!!!

Answer 5

Set \(g'(x)=0\) and solve for x and f \(g''(x)< 0 \) at this critical value, then g(x) is a maximum at that point.

Here's a plot.

Answer 6

http://www.wolframalpha.com/input/?i=g%28x%29+%3D+7+%2F+%28x%5E2+%2B+5%29

Answer 7

Oh I see now!

Answer 8

Here is \(g''(x)\) at that critical point - http://www.wolframalpha.com/input/?i=d%5E2%2Fdx%5E2+%28+7+%2F+%28x%5E2+%2B+5%29%29+

Answer 9

Oh ok so the minimum value would be somewhere around .55?

Answer 10

While the maximum is 1.4?

Answer 11

Yes

http://www.wolframalpha.com/input/?i=d+%2Fdx+%28+7+%2F+%28x%5E2+%2B+5%29+%29