1.

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Math 110 Course Resources - Curve Sketching Course Packet onintervals of concavity

Suppose thesecond derivativeoffis given byf''(x) =

9(x²+25)

(x²16)³

. Determine the intervals of concavity off. Enter your answer using interval notation. If an answer does not exist, enter DNE. fis concave up on

fis concave down on

2.

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Math 110 Course Resources - Curve Sketching Course Packet onintervals of concavity

Suppose thesecond derivativeoffis given byf''(x) =5x⁸(x+7)⁷(x²+81). Determine the intervals of concavity off. Enter your answer using interval notation. If an answer does not exist, enter DNE. fis concave up on

fis concave down on

3.

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Math 110 Course Resources - Curve Sketching Course Packet onintervals of concavity

Suppose thesecond derivativeoffis given byf''(x) =35x⁷(x2)⁵(x²+81). Determine the intervals of concavity off. Enter your answer using interval notation. If an answer does not exist, enter DNE. fis concave up on

fis concave down on

4.

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Math 110 Course Resources - Curve Sketching Course Packet onintervals of concavity

Suppose thesecond derivativeoffis given byf''(x) =5(x3)⁶(x²64). Determine the intervals of concavity off. Enter your answer using interval notation. If an answer does not exist, enter DNE. fis concave up on

fis concave down on

5.

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Math 110 Course Resources -Video Tutorial

Givenf(5) =15,f'(5) =9, andf''(x) = 0 forx5, which one of the following statements aboutf(11) must be true?

f(11) must be equal to3

f(11) must be greater than39

f(11) must be equal to21

f(11) must be less than21

f(11) must be equal to39

6.

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Math 110 Course Resources -Video Tutorial

Givenf(2) =25,f'(2) =7, andf''(x)<0 forx2, which one of the following statements aboutf(6) must be true?

f(6) must be less than-3

f(6) must be greater than-3

f(6) must be less than-10

f(6) must be equal to-24

f(6) must be greater than-24

7.

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Math 110 Course Resources - Curve Sketching Course Packet oninflection points

Consider the functionf(x) =3x⁵75x⁴+41x22. Enter the number of inflection points off(x).

Determine thex-coordinates of the inflection points. Enter your answer as a comma-separated list of values. The order of the values does not matter. Enter DNE iff(x) does not have any inflection points.

8.

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Math 110 Course Resources - Curve Sketching Course Packet oninflection points

Consider the functionf(x) =3x⁵40x³+17x42. Enter the number of inflection points off(x).

Determine thex-coordinates of the inflection points. Enter your answer as a comma-separated list of values. The order of the values does not matter. Enter DNE iff(x) does not have any inflection points.

9.

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Math 110 Course Resources - Curve Sketching Course Packet oninflection points

The following graph corresponds tof''(x),the second derivative off(x). If the graph does not appear, please reload the page.

Based on the above graph of the second derivative off(x), determine the number inflection points off(x). You may assume thatf''(x) is continuous,f''(x) is defined for allx, andf''(x) = 0 only whenx=7,x=0, andx=6. Enter the number of inflection points off(x):

Determine thex-coordinates of the inflection points. Enter your answer as a comma-separated list of values. The order of the values does not matter. Enter DNE iff(x) does not have any inflection points.

10.

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Math 110 Course Resources - Curve Sketching Course Packet onpoints of diminishing & increasing returns

The total monthly revenueR(x) generated from sales of Calculus videos is related to the amountxspent on advertising by R(x)=5x³+60x²+90x+70 wherexis in thousands of dollars. Calculate the point of diminishing returns for advertising costs. The point of diminishing returns occurs atx= . This means that if more than dollars is spent on advertising, then each additional dollar spent produces a

---Select--- smaller larger return on investment than the previous dollar.

11.

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Math 110 Course Resources - Curve Sketching Course Packet onpoints of diminishing & increasing returns

The total monthly revenueR(x) generated from sales ofMath t-shirtsis related to the amountxspent on advertising by R(x)=3x³18x²+81x+80 wherexis in thousands of dollars and 0x4. Which one of the following statements is true?

$2000is a point of increasing returns.

There are no points of increasing or diminishing returns.

$1000is a point of increasing returns.

$2000is a point of diminishing returns.

$1000is a point of diminishing returns.

12.

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Math 110 Course Resources - Curve Sketching Course Packet onclassifying critical points using the second derivative test

Use the second derivative test to determine thex-coordinates of the relative extrema of the functiong(x) =x⁴4x³36x²+ 5. Enter each answer as a comma-separated list of values. The order of the values does not matter. Enter DNE ifg(x) does not have any relative maximum or minimum values, respectively. x-coordinates of the relativemaxima=

x-coordinates of the relativeminima=

13.

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Math 110 Course Resources - Curve Sketching Course Packet onclassifying critical points using the second derivative test

Use the second derivative test to determine thex-coordinates of the relative extrema of the functiong(x) =5x+

2

x

. Enter each answer as a comma-separated list of values. The order of the values does not matter. Enter DNE ifg(x) does not have any relative maximum or minimum values, respectively. x-coordinates of the relativemaxima=

x-coordinates of the relativeminima=

14.

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Math 110 Course Resources - Curve Sketching Course Packet onclassifying critical points using the second derivative test

Use the second derivative test to determine thex-coordinates of the relative extrema of the functiong(x) =6x²+

324

x

. Enter each answer as a comma-separated list of values. The order of the values does not matter. Enter DNE ifg(x) does not have any relative maximum or minimum values, respectively. x-coordinates of the relativemaxima=

x-coordinates of the relativeminima=

15.

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MY NOTES

Determine whether each statement is true or false. You have one submission for each statement. (a)f(x) is concave up on the interval (a,b) iff''(x) > 0 on (a,b).True False

(b)f(x) is concave up on the interval (a,b) iff'(x) is increasing on (a,b).True False

(c)f(x) has an inflection point atx=cifx=cis in the domain off(x) andf''(c) = 0.True False

(d)f(x) has a relative minimum atx=ciff''(c) > 0.True False

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