H=√(f(x)) Find H'(1)

Question

f(1)=4, f(2)=3, f(3)=7

f '(1)=5, f '(2)=6, f '(3)=3/2

Answer 1

H = f(x)^1/2

so H'(x) = [1 / (2 * sqrt( f(x) ) ) ] * f'(x) by the chain rule aka dH/dx = (dH/df)*(df/dx)

so H'(1) = 1 / (2 * sqrt( f(1) ) ) ] *f'(1)

= 1 / (2 * sqrt(4) ) ] *5

= (1/4)*5 = 5/4