# For what values of x is #f(x)= e^x/(5x^2) +1# concave or convex?

The function is convex for

Calculate the first and second derivatives

is

As the discriminant is negative, the second derivative

The variation chart is as follows

graph{e^x/(5x^2)+1 [-9.71, 10.29, -1.96, 8.04]}

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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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