Suppose h(x)= sqrt(f(x)) and the equation of the tangent line to f(x) at x=1 is y=4+5(x−1).

Question

Find h′(1).

Answer 1

we know that f(1) = 4, since the tangent line touches the graph there.

h = √f
dh/dx = 1/(2√f) df/dx

we know that df/dx=5 from the equation of the line. So,

dh/dx = 1/(2√4) * 5 = 5/4