# Find {eq}f {/eq}. {eq}f'(x) = 1 + 3 \sqrt{x}; f(4) = 25 {/eq}

## Question:

Find {eq}f {/eq}.

{eq}f'(x) = 1 + 3 \sqrt{x}; f(4) = 25 {/eq}

## Finding Function Using Integration:

When the derivative of a function is given and the derivative is only the function of {eq}x {/eq}, then the function will be calculated by integrating the derivative with respect to {eq}x {/eq}. We get a constant after integration and will be calculated on the basis of initial conditions.

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Consider {eq}f'(x) = 1 + 3 \sqrt{x}\,\,\cdots(1) {/eq} and {eq}f(4) = 25 {/eq}.

Integrate the equation (1) with respect to {eq}x {/eq}.

{eq}\begi...