suppose df/dx=4x^1/2. If f(4)=21, then f(x)=?

Answer 1

Calculate the antiderivative:

f(x) = ∫ 4x^1/2 dx

f(x) = (²/₃)(4x^3/2) + C now use f(4) = 21 to calculate C

21 = (²/₃)(4(4)^3/2) + C

C = -¹/₃

Therefore, f(x) = ⁸/₃x^3/2 - ¹/₃