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Find the slope of the tangent line to the graph f(x)=\sin ^{2}x when x=\pi .

Again, take the derivative of the function and plug in \pi for x and that will give you the slope of the tangent line at x=\pi .

f'(x)=2\sin x\cos x\,


f'(\pi )=2\sin(\pi )\cos(\pi )=0\,

Thus, if we were to draw the tangent line to f(x)=\sin ^{2}x at x=\pi , the line would be a horizontal line with slope 0.

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