/
/
/
Find any inflection points given the equation. 1) f(x) = 5x^2 + 10x
Not my Question
Flag Content

# Question : Find any inflection points given the equation. 1) f(x) = 5x^2 + 10x : 2151709

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find any inflection points given the equation.

1) f(x) = 5x2 + 10x

A) Inflection point at (-2,-10)

B) No inflection points

C) Inflection point at (-1,-5)

D) Inflection point at (2,-10)

2) f(x) = 2x3 + 15x2 + 24x

A) No inflection points

B) Inflection points at (-1, -11), (-4, 16)

C) Inflection point at (- (5/2), (5/2))

D) Inflection point: (0, 0)

3) f(x) = (6x/x2 + 1)

A) Inflection points at (-1, -3), (1, 3)

B) No inflection points

C) Inflection points at (0, 0), (-1√(3), - (3/2)√(3)), (1√(3), (3/2)√(3))

D) Inflection points at (0, 0), (-1, -3), (1, 3)

4) f(x) = ex - 6e-x - 7x

A) Inflection point at (2, -6)

B) Inflection point at ((1/2) ln 6, - (7/2) ln 6)

C) Inflection point at (0, -5)

D) Inflection point at (ln 6, 5 - 7 ln 6)

5) f(x) = ln(12 - x2)

A) No inflection points

B) Inflection point at (-ln 12, 0)

C) Inflection point at (0, -ln 12)

D) Inflection point at (0, ln 12)

Suppose that the function with the given graph is not f(x), but f'(x). Find the open intervals where the function is concave upward or concave downward, and find the location of any inflection points.

6) A) Concave upward on (-∞, -2) and (2, ∞); concave downward on (-2, 2); inflection points at -120 and 120

B) Concave upward on (-∞, 0); concave downward on (0, ∞); inflection point at 0

C) Concave upward on (-∞, -2) and (2, ∞); concave downward on (-2, 2); inflection points at -2 and 2

D) Concave upward on (-2, 2); concave downward on (-∞, -2) and (2, ∞); inflection points at -2 and 2

7) A) Concave upward on (-∞, 0); concave downward on (0, ∞); inflection point at 0

B) Concave upward on (-2, 2); concave downward on (-∞, -2) and (2, ∞); inflection points at -120 and 120

C) Concave upward on (-2, 2); concave downward on (-∞, -2) and (2, ∞); inflection points at -2 and 2

D) Concave upward on (-∞, -2) and (2, ∞); concave downward on (-2, 2); inflection points at -2 and 2

8) A) Concave upward on (-3, 3); concave downward on (-∞, -3) and (3, ∞); inflection points at -3 and 3

B) Concave upward on (-∞, -3) and (3, ∞); concave downward on (-3, 3); inflection points at -3 and 3

C) Concave upward on (-∞, -3) and (3, ∞); concave downward on (-3, 3); inflection points at -20 and 20

D) Concave upward on (-∞, 0); concave downward on (0, ∞); inflection point at 0

9) A) Concave upward on (-1, 0) and (1, ∞); concave downward on (-∞, -1) and (0, 1); inflection points

at -2, 0, and 2

B) Concave upward on (-∞, 0); concave downward on (0, ∞); inflection point at 0

C) Concave upward on (-∞, -1) and (0, 1); concave downward on (-1, 0) and (1, ∞; ); inflection points

at -1, 0, and 1

D) Concave upward on (-1, 0) and (1, ∞); concave downward on (-∞, -1) and (0, 1); inflection points

at -1, 0, and 1

Decide if the given value of x is a critical number for f, and if so, decide whether the point is a relative minimum, relative maximum, or neither.

10) f(x) = -x2 - 16x - 64; x = 8

A) Critical number but not an extreme point

B) Not a critical number

C) Critical number, relative maximum at (8, -144)

D) Critical number, relative minimum at (8, -144)

11) f(x) = x5; x = 0

A) Critical number, relative minimum at (0, 0)

B) Critical number but not an extreme point

C) Not a critical number

D) Critical number, relative maximum at (0, 0)

12) f(x) = (x2 - 6)(2x - 3); x = (1/2)

A) Critical number, relative minimum at ((1/2), (23/2))

B) Critical number but not an extreme point

C) Critical number, relative maximum at ((1/2), (23/2))

D) Not a critical number

13) f(x) = 2x3 - 3x2 - 12x + 18; x = 2

A) Not a critical number

B) Critical number but not an extreme point

C) Critical number, relative minimum at (2, -2)

D) Critical number, relative maximum at (2, -2)

14) f(x) = 3x4 - 4x3 - 12x2 + 24; x = 0

A) Critical number, relative minimum at (0, 24)

B) Critical number, relative maximum at (0, 24)

C) Not a critical number

D) Critical number but not an extreme point

15) f(x) = 4x5 - 5x4; x = 1

A) Critical number but not an extreme point

B) Not a critical number

C) Critical number, relative maximum at (1, -1)

D) Critical number, relative minimum at (1, -1)

16) f(x) = x2 - x - 6; x = (1/2)

A) Critical number but not an extreme point

B) Critical number, relative minimum at ((1/2),- (25/4))

C) Not a critical number

D) Critical number, relative maximum at ((1/2),- (25/4))

17) f(x) = (x + 3)4; x = -3

A) Critical number; relative maximum at (-3, 0)

B) Critical number but not an extreme point

C) Not a critical number

D) Critical number; relative minimum at (-3, 0)

18) f(x) = x19/9 + x10/9; x = (10/19)

A) Critical number but not an extreme point

B) Critical number, relative maximum at ((10/19), 0)

C) Not a critical number

D) Critical number, relative minimum at ((10/19), 0)

Solve the problem.

19) The percent of concentration of a certain drug in the bloodstream x hours after the drug is administered is given by K(x) = (3x/x2 + 36). At what time is the concentration a maximum?

A) 3.6 hr

B) 1.8 hr

C) 3 hr

D) 6 hr

20) Find the point of diminishing returns (x, y) for the function R(x) = 10,000 - x3 + 45x2 + 700x, 0 ≤ x ≤ 20, where R(x) represents revenue in thousands of dollars and x represents the amount spent on advertising in tens of thousands of dollars.

A) (66.41, -37,937.27)

B) (15 , 27,250)

C) (14 , 25,876)

D) (18, 31,348)

21) The population of a certain species of fish introduced into a lake is described by the logistic equation

G(t) = (12,000/1 + 19e-1.2t) ,

where G(t) is the population after t years. Find the point at which the growth rate of this population begins to decline.

A) (3.37, 9000)

B) (3.53, 6000)

C) (4.85, 9000)

D) (2.45, 6000)

The function gives the distances (in feet) traveled in time t (in seconds) by a particle. Find the velocity and acceleration at the given time.

22) s = (1/t + 2), t = 2

A) v = - (2/64) ft/s, a = (1/16) ft/s2

B) v = (2/64) ft/s, a = - (1/16) ft/s2

C) v = (1/16) ft/s, a = - (2/64) ft/s2

D) v = - (1/16) ft/s, a = (2/64) ft/s2

23) s = 2t3 + 6t2 + 5t + 4, t = 3

A) v = 54 ft/s, a = 30 ft/s2

B) v = 30 ft/s, a = 54 ft/s2

C) v = 95 ft/s, a = 48 ft/s2

D) v = 48 ft/s, a = 95 ft/s2

24) s = 4t3 + 6t2 + 3t + 4, t = 1

A) v = 36 ft/s, a = 27 ft/s2

B) v = 24 ft/s, a = 0 ft/s2

C) v = 27 ft/s, a = 36 ft/s2

D) v = 0 ft/s, a = 24 ft/s2

25) s = -5t3 + 3t2 - 8t - 2, t = 1

A) v = -24 ft/s, a = -17 ft/s2

B) v = -17 ft/s, a = 1 ft/s2

C) v = 1 ft/s, a = -17 ft/s2

D) v = -17 ft/s, a = -24 ft/s2

26) s = √(t2 - 5), t = 3

A) v = - (3/2) ft/s, a = (5/8) ft/s2

B) v = - (5/8) ft/s, a = (3/2) ft/s2

C) v = (5/8) ft/s, a = - (3/2) ft/s2

D) v = (3/2) ft/s, a = - (5/8) ft/s2

Provide the proper response.

27) True or false? If the graph of a function f is concave down on its entire domain, then f' is decreasing.

A) True

B) False

28) True or false? If the graph of a function f is concave down on its entire domain, then f' is increasing.

A) True

B) False

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

29) Explain why every polynomial function of the form

f(x) = ax3 + bx2 + cx + d, a ≠ 0, must have exactly one point of inflection.

30) Show that a function of the form

f(x) = ax4 + bx3 + cx2 + dx + e has no points of inflection whenever 8ac > 3b2.

31) You are applying the second derivative test and you find that f'(a) = 0 and f''(a) = 0. What does that tell you? What would be your next step?

32) Give an example of a function for which the first derivative is always positive and the second derivative is always negative.

33) Give an example of a function for which the first derivative is always negative and the second derivative is always positive.

34) Give an example of a function for which the first derivative and the second derivative are both always positive.

35) Give an example of a function for which the first derivative and the second derivative are both always negative.

## Solution 5 (1 Ratings )

Solved
Calculus 4 Months Ago 52 Views