# Let #f(x)=(5/2)sqrt(x)#. The rate of change of f at #x=c# is twice its rate of change at #x=3#. What is the value of c?

We start by differentiating, using the product rule and the chain rule.

Now, by the product rule;

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The value of ( c ) is ( 36 ).

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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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