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Let f be a function such that f(x+y)=f(x...

Let f be a function such that `f(x+y)=f(x)+f(y)" for all "x and y and f(x) =(2x^(2)+3x) g(x)" for all "x, " where "g(x)` is continuous and g(0) = 3. Then find f'(x)

Text Solution

Verified by Experts

The correct Answer is:
9
`f'(x)=underset(hrarr0)lim(f(x+h)-f(x))/(h)`
`=underset(hrarr0)lim(f(x)+f(h)-f(x))/(h)`
`=underset(hrarr0)lim(f(h))/(h)`
`=underset(hrarr0)lim((2h^(2)+3h)g(h))/(h)`
`=underset(hrarr0)lim(2h+3)g(h)`
`=(0+3)g(0)`
`=3g(0)`
`=3xx3`
`=9`
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