Function from a derivative of the form kx over the square root of a quadratic, using a known value

Function from a derivative of the form kx over the square root of a quadratic, using a known value

5 marks

The derivative of a function \(f\) is \(f'(x)=\dfrac{10x}{\sqrt{5x^2+9}}\), and \(f(0)=4\). Find an expression for \(f(x)\).[5]

Solution:

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Answer:\(f(x)=2\sqrt{5x^2+9}-2\)

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