# How do you find an equation for the function #f'(x)=sin4x# whose graph passes through the point (pi/4,-3/4)?

Integrate both sides.

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To find an equation for the function f'(x) = sin(4x) that passes through the point (π/4, -3/4), we can integrate the given function to find the original function f(x).

Integrating f'(x) = sin(4x) with respect to x, we get: f(x) = -1/4 * cos(4x) + C

To determine the value of C, we substitute the given point (π/4, -3/4) into the equation: -3/4 = -1/4 * cos(4(π/4)) + C

Simplifying the equation: -3/4 = -1/4 * cos(π) + C -3/4 = -1/4 * (-1) + C -3/4 = 1/4 + C C = -1

Therefore, the equation for the function f(x) = -1/4 * cos(4x) - 1, which is the antiderivative of f'(x) = sin(4x), and it passes through the point (π/4, -3/4).

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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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