Computing Derivatives Exercises

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This question is asking what is the largest (and smallest) the derivative ever gets. Since f ' (x) = cos(x), the largest the derivative ever gets is 1. The smallest the derivative gets is -1.

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This question is asking what is the largest (and smallest) the derivative ever gets. Since f ' (x) = -sin(x), the largest the derivative ever gets is 1. The smallest the derivative gets is -1.

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The graph of -sin x looks like this:

We can see its derivative will be 0 at  and :

And from the discussion earlier, the largest its slope will be is 1 and the smallest is -1. We can see from the picture where these largest and smallest slopes happen:

This lets us plot some points for the derivative function:

and if we connect the dots in a nice smooth curve, we find the graph of -cos x:

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The graph of -cos x looks like this:

We can see where its slope is 0, and where its slope is largest and smallest:

We plot some points on the graph of the derivative:

and play connect the dots to find the graph of sin x:

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• f ' (x) = cos(x)

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• g ' (z) = -sin(z)

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• h ' (y) = -cos(y)

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• r ' (k) = sin(k)