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Popular Calculus >

f^'(x)=6x,f(0)=8

Solution

f^{^{'}} (x) = 6 x, f (0) = 8

Solution

f (x) = 3 x^{2} + 8

Solution steps

f^{'} (x) = 6 x

If

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

f (x) = \int 6 x d x

\int 6 x d x = 3 x^{2} + c_{1}

f (x) = 3 x^{2} + c_{1}

Apply initial conditions:

f (x) = 3 x^{2} + 8

f (x) = 3 x^{2} + 8

Graph

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Frequently Asked Questions (FAQ)

What is the solution for f^'(x)=6x,f(0)=8 ?
The solution for f^'(x)=6x,f(0)=8 is f(x)=3x^2+8