Answer:
[tex]f(x) = 3x^2+8[/tex]
Step-by-step explanation:
We are given the first derivative of [tex]f(x)[/tex] and the value of [tex]f(0)[/tex].
To go from the first derivative to the original function, we integrate.
Therefore:
[tex]f(x) = \int {6x} \, dx[/tex]
To integrate, we add 1 to the power and divide by the new power:
[tex]\int {6x} \, dx = \frac{6x^2}{2} =3x^2+C[/tex]
Because we have an indefinite integral, we have to add the constant, [tex]c[/tex], to the end.
So: [tex]f(x) = 3x^2+C[/tex]
We know [tex]f(0)[/tex] so we can find the constant [tex]C[/tex].
[tex]f(0)=3(0)^2+C=8[/tex]
[tex]C=8[/tex]
Therefore [tex]f(x) = 3x^2+8[/tex]
