What is the solution for f^'(x)=8x^3-6x^2+10x-9,f(1)=24 ?

The solution for f^'(x)=8x^3-6x^2+10x-9,f(1)=24 is f(x)=2x^4-2x^3+5x^2-9x+28

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f^'(x)=8x^3-6x^2+10x-9,f(1)=24

f^{^{'}} (x) = 8 x^{3} - 6 x^{2} + 10 x - 9, f (1) = 24

f (x) = 2 x^{4} - 2 x^{3} + 5 x^{2} - 9 x + 28

Solution steps

f^{'} (x) = 8 x^{3} - 6 x^{2} + 10 x - 9

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

then

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

f (x) = \int 8 x^{3} - 6 x^{2} + 10 x - 9 d x

\int 8 x^{3} - 6 x^{2} + 10 x - 9 d x = 2 x^{4} - 2 x^{3} + 5 x^{2} - 9 x + c_{1}

f (x) = 2 x^{4} - 2 x^{3} + 5 x^{2} - 9 x + c_{1}

Apply initial conditions:

f (x) = 2 x^{4} - 2 x^{3} + 5 x^{2} - 9 x + 28

f (x) = 2 x^{4} - 2 x^{3} + 5 x^{2} - 9 x + 28

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What is the solution for f^'(x)=8x^3-6x^2+10x-9,f(1)=24 ?
The solution for f^'(x)=8x^3-6x^2+10x-9,f(1)=24 is f(x)=2x^4-2x^3+5x^2-9x+28