What is the solution for f^{''}(x)=2,f^'(2)=5,f(3)=2 ?

The solution for f^{''}(x)=2,f^'(2)=5,f(3)=2 is f(x)=x^2+x-10

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f^{''}(x)=2,f^'(2)=5,f(3)=2

f^{^{''}} (x) = 2, f^{^{'}} (2) = 5, f (3) = 2

f (x) = x^{2} + x - 10

Solution steps

f^{''} (x) = 2

Solve

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

Solve

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

Apply initial conditions:

f (x) = x^{2} + x - 10

f (x) = x^{2} + x - 10

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What is the solution for f^{''}(x)=2,f^'(2)=5,f(3)=2 ?
The solution for f^{''}(x)=2,f^'(2)=5,f(3)=2 is f(x)=x^2+x-10