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

The solution for f^{''}(x)=2,f^'(2)=5,f(2)=10 is f(x)=x^2+x+4

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f^{''}(x)=2,f^'(2)=5,f(2)=10

f^{^{''}} (x) = 2, f^{^{'}} (2) = 5, f (2) = 10

f (x) = x^{2} + x + 4

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 + 4

f (x) = x^{2} + x + 4

What is the solution for f^{''}(x)=2,f^'(2)=5,f(2)=10 ?
The solution for f^{''}(x)=2,f^'(2)=5,f(2)=10 is f(x)=x^2+x+4