What is the solution for f^'(x)=6x^2-8x,f(3)=27 ?

The solution for f^'(x)=6x^2-8x,f(3)=27 is f(x)=2x^3-4x^2+9

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f^'(x)=6x^2-8x,f(3)=27

f^{^{'}} (x) = 6 x^{2} - 8 x, f (3) = 27

f (x) = 2 x^{3} - 4 x^{2} + 9

Solution steps

f^{'} (x) = 6 x^{2} - 8 x

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

then

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

f (x) = \int 6 x^{2} - 8 x d x

\int 6 x^{2} - 8 x d x = 2 x^{3} - 4 x^{2} + c_{1}

f (x) = 2 x^{3} - 4 x^{2} + c_{1}

Apply initial conditions:

f (x) = 2 x^{3} - 4 x^{2} + 9

f (x) = 2 x^{3} - 4 x^{2} + 9

x \to - 9 lim (\frac{- 3 x}{x + 9})

\frac{d}{d t} (a sin^{3} (t))

\frac{d ^{2}}{d x ^{2}} (x - \frac{2}{x})

\frac{\partial}{\partial y} (x^{2} - x y - y^{2})

\int \frac{3 x ^{3} - x}{x} d x

What is the solution for f^'(x)=6x^2-8x,f(3)=27 ?
The solution for f^'(x)=6x^2-8x,f(3)=27 is f(x)=2x^3-4x^2+9