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Find a function f(x) such that f'(x)=8x^2+5  and f (0) =1

 

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 Jun 24, 2020
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Find a function f(x) such that f'(x)=8x^2+5  and f (0) =1

 

You are looking for the antiderivative of f'(x)

 

The antiderivative of x2  is  x3/3,  that of x0 is x1/1  (Note that x0 is just 1 and x1/1 is just x).  

 

So f(x) = 8x3/3 + 5x + k  where k is a constant to be found by using the fact that f(0) = 1.

 Jun 25, 2020

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