# Is #f(x) =(x-1)^3/(x^2-2)# concave or convex at #x=8#?

f(x) is convex at x=8

Differentiating with respect to x,

This function, the derivative, will tell us the slope/gradient of the function at any point x

If we then differentiate again with respect to x,

This function, the second derivative, will tell us the curvature of the function at any point (i.e. whether it is concave or convex)

Hence f(x) is convex at x=8

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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