f(8)=7, f’(8)=-8 and H(x)=(1+f(x))^3 Find dH/dx|x=8

Answer 1

f(8) = 7

f’(8) = -8

H(x) = (1 + f(x))³

Differentiate using chain rule and exponent rule:

H'(x) = 3(1 + f(x))² * f'(x)

Find dH/dx at x = 8:

H'(8) = 3(1 + f(8))² * f'(8) = 3(1 + 7)² * (-8) = -24(8)² = -24 * 64 = -1536