Q1. Limit = 3Q2. Graph (example)

Q4.2QToQ6.25x2 -7ox+ 4908. (x - 2)(xz + 2x + 4)Q9. Graph (tangent)

Q3. Graph. Y = tan x

Q5.3x2 -2x-8Q7. log 6

Q10. Graph (secant)

3. Ouartic Function Problem I

a. Graph. h(x) = xa - Zxa - 9x2 + 20x + 80

j./-2

b. The h' graph looks like a cubic function graph.Conjecture: Seventh-degree lunction has a sixth-degree function for its derivative.

c. By plotting the graph using a friendly window, thentracing, the zeros of h' are -2, 1, 2.5.

d. lf h'(x) = 0, the h graph has a high point or a lowpoint. This is reasonable because if h'(x) = Q, thgrate ol change of h(x) is zero, which would happenwhen the graph stops going up and starts goingdown, or vice versa.

e. See graph in part a.

4. Quartic Function Problem llGraph. g(x) = -xa + 8x3 - 24x2 + 32x - 25

1. Cubic Function Problem I

a. Graph. f(x) = -x3 + 12x + 25, and f'

,'t2

b. f'(x) is positive lor -2 < x < 2.The graph of I is increasing for these x-values.

c. f(x) is decreasing for x satisfying lxl > 2. f'(x) < 0 forthese values of x.

d. Where the f' graph crosses the x-axis, the f graphhas a high point or a low point.

e. See the graph in part a.f. Coniecture: f is ouadratic.

2. Cubic Function Problem llGraph. f(x) = x3 -2x2 + 2x- 15

rutts',,'

s

The graph does not have the high and low points thatare typical of a cubic function. As x increases, thegraph starts to roll over and form a high point, but itstarts going back up again before that happens. Thisbehavior is revealed by the fact that the derivative ispositive everywhere. Between x = 0 and x = 1 thederivative reaches a low point, indicating that the slopeis a minimum, but the slope is still positive and thegraph of g is still going up.

The graph does not have the expected shape for aquartic function. The two high points and the lowpoint all appear to occur as a high point at x = 2. Thederivative graph crosses the x-axis just once, atx = 2, indicating that this is the only place where thefunction graph is horizontal.

Problem Set 3-3 Solutions Monuol 29