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The derivative of f(x) = \sin{x} is f'(x) = \cos{x}. Evaluate this at x = \frac{\pi}{2} to get f'(\frac{\pi}{2}) = \cos{(\frac{\pi}{2})} = 0.
Answer for screen readers
The derivative of f(x) = \sin{x} is f'(x) = \cos{x}. Evaluate this at x = \frac{\pi}{2} to get f'(\frac{\pi}{2}) = \cos{(\frac{\pi}{2})} = 0.
More Information
For the graph of a function to have a horizontal tangent line, the derivative must be zero at that point. For \sin{x}, this occurs at certain multiples of \pi.
Tips
A common mistake is to evaluate the function instead of its derivative at the point.
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