suppose... f(4)=5, f′(4)=2, f(7)=2, f′(7)=−7, and H(x)=f(x^2 −9) find derivative at x=4 H'(4)=????

Answer 1

This question is testing your knowledge of the chain rule.

H(x) = f(x² - 9)

This means that H'(x) = f'(x² - 9) * (x² - 9)'. This is coming from the chain rule

H'(x) = f'(x² - 9) * 2x

H'(4) = f'(16-9)* 2(4) = f'(7)*8

H'(4) = -7*8 = -56