q′ = 0 if x = 3. Since q′ is negative to the left of x = 3 and positive to the
right, the minimum value of q occurs at x = 3.(A) The best approximation for when h is small is the local linear
(or tangent line) approximation. If we let , then
and . The approximation for f(h) is f(0) + f ′(0)
· h, which equals .(A) Since f ′(x) = e−x(1 − x), f ′(0) > 0.(E) The graph shown serves as a counterexample for A−D.(D) Since .(E) We differentiate implicitly: 3x^2 + x^2 y′ + 2 xy + 4 y′ = 0. Then . At .