Question

Find f.


f ''(x) = 8 − 18x, f(0) = 7, f(2) = 11

Answer 1

you can integrate that twice

Answer 2

f''(x) = 4x^2 − 3x^3 +C

Answer 3

you should get two constants

Answer 4

like this?
f''(x) = 4x^2 − 3x^3 +Dx + C

Answer 5

$$\Large {
f ' ' (x) = 8 - 18x, \\
\\ \therefore \\
f (x) = 4x^2 - 3x^3+ C_1x + C_2\\
f(0) = 4(0)^2 - 3(0)^3+ C_1(0) + C_2 = 7 \\
\\ \therefore \\
C_2 = 7

}
$$