Find the specific antiderivative using the given information.

Question

f'(x) = 70(1 − 7x)^2/3 and f(−1) = 200

Answer 1

f'(x) = 70(1-7x)^(2/3) f(-1) =200

f(-1)=200 is used to find the constant term of the integral

f(x) = (3/5)70(1-7x)^(5/3)/(-7) + constant

f(x) =-6(1-7x)^(5/3) + c

f(-1) = -6(1+7)^(5/3) + c = 200

c = 200 + 6(2)^5 = 200

f(x) = 392 - 6(1-7x)^(5/3)