Suppose f(π/3) = 3 and f '(π/3) = −7, and let g(x) = f(x) sin(x) and h(x) = cos(x)/f(x). Find the following.

Question

Suppose f(π/3) = 3 and f '(π/3) = −7, and let g(x) = f(x) sin(x) and h(x) = cos(x)/f(x).

(a)    g'(π/3)=_______

(b)    h'(π/3)=_______

Answer 1

Simon,

Since g(x) is a product of 2 functions and h(x) is a quotient of 2 functions, you can use the product rule to find g'(x) and the quotient rule to find h'(x). Then just plug in π/3 for x.