# Find f. {eq}f"(x) = 6 - 18x, f(0) = 7, f(2) = 11 {/eq} {eq}f(x) = {/eq}

## Question:

Find f. {eq}f"(x) = 6 - 18x, f(0) = 7, f(2) = 11 {/eq}

{eq}f(x) = {/eq}

## Double Integration

In calculus, double integration is used in finding the volume of a solid defined by a function. It can also be used in finding the solution of a second order differential equation. In solving for the differential equation, initial conditions are given so that there will be no arbitrary constants and coefficients.

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We will integrate {eq}f''(x) {/eq} to get the equation for {eq}f'(x) {/eq}.

{eq}f"(x) = 6 - 18x \\ \displaystyle \frac{d(f'(x))}{dx} = 6 -...