Question

Find f.
f'(x)=(sqrt(x))(6+10x)
f(1)=11

Answer 1

It is a matter of integrating f′:


`f(x)=\int √(x)(6+10x)dx, \\ \\f(x)=\int 6x^(1/2)dx+\int10x^(3/2)dx, \\ \\f(x)=4x^(3/2)(x+1)+C.`

Combine the constants. Then use the initial condition to find C:


`11=8+C\implies C=3`

Therefore,


`f(x)=4x^(3/2)(x+1)+3.`