The flight path that satisfies the conditions in the following diagram is

y = 0.00001x³ + 0.0015x².

Find the inflection point of this path. (Assume

h = 5 miles.

Enter your answer as an ordered pair in the form x, y.)

Explain why the inflection point represents the point of steepest ascent of the airplane.The curve is decreasing before the inflection point and increasing after the inflection point. Therefore, the slope is maximized at the inflection point.The curve is increasing before the inflection point and decreasing after the inflection point. Therefore, the slope is maximized at the inflection point. The curve is concave down before the inflection point and concave up after the inflection point. Therefore, the slope is maximized at the inflection point.The curve is concave up before the inflection point and concave down after the inflection point. Therefore, the slope is maximized at the inflection point.none of these

The temperature in a refining tower is

f(x) = x⁴ 4x³ + 118

degrees Fahrenheit after

x

hours (for

0 x 5).

(a)Make a sign diagram for the first derivative.

---Select--- f '(x) > 0 f '(x) < 0 f '(x) = 0 undefined	---Select--- f '(x) > 0 f '(x) < 0 f '(x) = 0 undefined	---Select--- f '(x) > 0 f '(x) < 0 f '(x) = 0 undefined	---Select--- f '(x) > 0 f '(x) < 0 f '(x) = 0 undefined
x =		x =

Make a sign diagram for the second derivative.

---Select--- f ''(x) > 0 f ''(x) < 0 f ''(x) = 0 undefined	---Select--- f ''(x) > 0 f ''(x) < 0 f ''(x) = 0 undefined	---Select--- f ''(x) > 0 f ''(x) < 0 f ''(x) = 0 undefined	---Select--- f ''(x) > 0 f ''(x) < 0 f ''(x) = 0 undefined
x =		x =

(b)Sketch the graph of the revenue function, showing all relative extreme points and inflection points.

Give an interpretation of the inflection point.The decline in temperature first begins to accelerate at the inflection point.The temperature starts to increase at the inflection point. The decline in temperature first begins to slow at the inflection point.The temperature starts to decrease at the inflection point.none of these

A graphing calculator is recommended. Use a graphing calculator to estimate the x-coordinates of the inflection points of the function, rounding your answers to two decimal places. [Hint: Graph the second derivative, either calculating it directly or using NDERIV twice, and see where it crosses the x-axis. Enter your answers as a comma-separated list.]

f(x) = x⁵ 2x³ + 9x + 3

x=

For the function, find all critical numbers and then use the second-derivative test to determine whether the function has a relative maximum or minimum at each critical number. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x) = x³ 12x² + 21x 2

relative maximax=

relative minimax=

For the graph, which of the numbered points are inflection points? (Enter your answers as a comma-separated list.)

The xy-coordinate plane is given. The curve enters the window on the positive y-axis, goes up and right becoming less steep, passes through a point labeled 1, continues up and right becoming less steep, changes direction at a point labeled 2, goes down and right becoming more steep, passes through a point labeled 3, goes down and right becoming less steep, changes direction at a point labeled 4, goes up and right becoming more steep, passes through a point labeled 5, goes up and right becoming less steep, changes direction at a point labeled 6, goes down and right becoming more steep, passes through a point labeled 7, continues down and right becoming more steep, and ends above the x-axis.