Let Px FxGx and Qx FxGx where F and G are the functions wh

Let P(x) = F(x)G(x) and Q(x) = F(x)/G(x), where F and G are the functions whose graphs are shown.

FindP\'(2).

Find Q\' (7)

Solution

The slope\'s are pretty easy to see but this is an exercise in derivation rules A) u\'(x) = g(x)f\'(x) + f(x)g\'(x) -- this is the multiplication rule u\'(1) = g(1)f\'(1) + f(1)g\'(1) -- find these values by looking on the graph, remembering that the derivatives are just the slopes of the lines u\'(1) = 1(2) + 2(-1) = 2 - 2 = 0 B) v\'(x) = [g(x)f\'(x) - f(x)g\'(x)] / g(x)² -- this is the quotient rule v\'(1) = [1(2) - 2(-1)] / 1² = 2 + 2 = 4