wolfram Recall that given a function f we have defined the d

wolfram

Recall that, given a function f we have defined the derivative function of f, written as f(x), by f\'(x) = lim_h rightarrw 0 f(x+h)-f(x)/h For any specific value a, f\'(a) will represent the slope of the tangent line to the curve y = f(x) at the point (a,f(a)). Consider the functions f and g graphed below: Let q(x) = f(x)g(x). Find each of the following: q\'(-5) q\'(-2) q\'(0) q\'(4)

Solution

a) q\'(-5) = f\'(-5) g(-5) + f(-5)g\'(-5) using multiplication rule

b) q\'(-2) = f\'(-2) g(-2) + f(-2)g\'(-2) using multiplication rule

c) q\'(0) = f\'(0) g(0) + f(0)g\'(0) using multiplication rule

d) q\'(4) = f\'(4) g(4) + f(4)g\'(4) using multiplication rule