8.

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Math 110 Course Resources - Curve Sketching Course Packet oncritical points

(a) Consider the functionf(x) = (5x+ 8)(3x+ 5). Enter the number of critical points/numbers off(x).

Determine thex-coordinates of the critical 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 critical points.

(b) Consider the functiong(x) =

5x+ 8

3x+ 5

. Enter the number of critical points/numbers ofg(x).

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

9.

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Math 110 Course Resources - Curve Sketching Course Packet oncritical points

Consider the functionf(x) = (7x+ 1)^1/3. Enter the number of critical points/numbers off(x).

Determine thex-coordinates of the critical 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 critical points.

0

10.

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Math 110 Course Resources - Curve Sketching Course Packet oncritical points

Consider the functionf(x) =

7x²+5

x²36

. Enter the number of critical points/numbers off(x).

Determine thex-coordinates of the critical 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 critical points.

0

11.

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Math 110 Course Resources - Curve Sketching Course Packet oncritical points

Consider the functionf(x) =x

x2+9

. Enter the number of critical points/numbers off(x).

Determine thex-coordinates of the critical 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 critical points.

12.

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Math 110 Course Resources - Curve Sketching Course Packet oncritical points

Consider the functionf(x) =3

x

2

x

+8. Enter the number of critical points/numbers off(x).

Determine thex-coordinates of the critical 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 critical points.

13.

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Math 110 Course Resources - Curve Sketching Course Packet oncritical points

Consider the functionf(x) = (2x²1)^2/3. Enter the number of critical points/numbers off(x).

Determine thex-coordinates of the critical 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 critical points.

14.

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Math 110 Course Resources - Curve Sketching Course Packet oncritical points

(a) Consider the functionf(x) =

x24

. Enter the number of critical points/numbers off(x).

Determine thex-coordinates of the critical 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 critical points.

(b) Consider the functiong(x) =

4x2

. Enter the number of critical points/numbers ofg(x).

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

15.

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Math 110 Course Resources - Curve Sketching Course Packet oncritical points

Consider the functionf(x) =9x+

5

x

+4. Enter the number of critical points/numbers off(x).

Determine thex-coordinates of the critical 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 critical points.

16.

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Math 110 Course Resources - Curve Sketching Course Packet oncritical points

Consider the functionf(x) =4x³21x²24x+ 9. Enter the number of critical points/numbers off(x).

Determine thex-coordinates of the critical 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 critical points.

17.

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Math 110 Course Resources - Curve Sketching Course Packet onrelative extrema - Curve Sketching Course Packet oncritical points

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

Based on the above graph off(x), determine the number critical points and relative extrema off(x). You may assume thatf(x) is continuous and defined for allxon the interval shown. Enter the number of critical points/numbers off(x): Enter the number of relative maxima off(x): Enter the number of relative minima off(x):

18.

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

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

Based on the above graph of the derivative off(x), determine the number critical points and relative extrema off(x). You may assume thatf'(x) is continuous,f'(x) is defined for allx, andf'(x) = 0 only whenx=7,x=0, andx=7. Enter the number of critical points/numbers off(x): Enter the number of relative maxima off(x): Enter the number of relative minima off(x):

19.

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

Determine thex-coordinates of the relative extrema of the functiong(x) =6x⁵90x³+26. 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=

20.

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

Determine thex-coordinates of the relative extrema of the functiong(x) =x⁴8x³32x²+ 1. 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=

21.

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

Determine thex-coordinates of the relative extrema of the functiong(x) =x⁴12x³+10. 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=

22.

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

Determine thex-coordinates of the relative extrema of the functiong(x) =

x²

4x5

. 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=