Maths P1 Differentiation question

Hi, I would like some help on the second part of this question please.
https://gyazo.com/360b74dd9b8a1e19bc9133ede1695830

So I found the second derivative and sub in x =2 since it's the minimum and gives a result of = 0. Not sure how to continue.
I know when second derivative gives me a positive or negative value it would be a minimum or maximum but not sure what it is when = 0.

Thanks

Original post by Jian17

Hi, I would like some help on the second part of this question please.
https://gyazo.com/360b74dd9b8a1e19bc9133ede1695830

So I found the second derivative and sub in x =2 since it's the minimum and gives a result of = 0. Not sure how to continue.
I know when second derivative gives me a positive or negative value it would be a minimum or maximum but not sure what it is when = 0.
Thanks

You are getting confused between layers of derivatives here.

For a function

f(x)

, we have that

\dfrac{d}{dx}f(x) = 0

tells us the critical points. The sign of

\dfrac{d^2}{dx^2}f(x)

tells us the nature of these points.

This question asks you to investigate the gradient. Therefore your function is the gradient function:

f(x) = x + 4x^{-2}

as told in the question.

The first derivative of this gives you the critical points, and the second derivative will tell you their nature.

So in the grand scheme of the question, it's