# Find f such that {eq}f'(x) = \frac{6}{\sqrt{x}},\; f(4) = 36. {/eq}

## Question:

Find f such that {eq}f'(x) = \frac{6}{\sqrt{x}},\; f(4) = 36. {/eq}

## Antiderivative:

The antiderivative is an important concept of mathematics that is applied in deriving a function from its derivative. If {eq}g'(x) {/eq} is the derivative of a function {eq}g(x) {/eq}, then the original function can be obtained by integrating the function {eq}g'(x) {/eq}.

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We have to find f such that {eq}f'(x) = \dfrac{6}{\sqrt{x}},\; f(4) = 36. {/eq}

\begin{align} f(x) &=\int f'(x)dx\\[0.3cm] &=\int ...