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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}.

Answer and Explanation: 1

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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 ...

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Antiderivative: Rules, Formula & Examples

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Chapter 8 / Lesson 12
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Understand what an antiderivative is and what antiderivative rules are. Use various antiderivative formulas and learn how to do antiderivatives. See the antiderivative chart for common functions and practice solving basic antiderivatives examples.


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