If f’(x) = 8x3 – 2x, f(2) = 8, find f(x).
Given f’(x) = 8x3 – 2x and f(2) = 8
On integrating the given equation, we have
We know
Recall
⇒ f(x) = 2x4 – x2 + c
On substituting x = 2 in f(x), we get
f(2) = 2(24) – 22 + c
⇒ 8 = 32 – 4 + c
⇒ 8 = 28 + c
∴ c = –20
On substituting the value of c in f(x), we get
f(x) = 2x4 – x2 + (–20)
∴ f(x) = 2x4 – x2 – 20
Thus, f(x) = 2x4 – x2 – 20