If f’(x) = 8x<sup

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