3 simple questions Cacl 1

Daniel Kevins

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Standard

Assessed

C

3.1MM

State whether a given point on a graph is a “global/local maximum/minimum”.

Question

For the function graphed below, determine whether the function has the extremum indicated at each

x-value in the table.

KdUd+7cuXXrVn0KQGW4aAYACBAXzQAAASJmAAABImYAAAEiZgAAgbnuuv8PJdcoPXKA8FMAAAAASUVORK5CYII=

x

Local minimum

Local maximum

Global minimum

Global maximum

−5

Yes

No

Yes

No

Yes

No

Yes

No

−2

Yes

No

Yes

No

Yes

No

Yes

No

1

Yes

No

Yes

No

Yes

No

Yes

No

5

Yes

No

Yes

No

Yes

No

Yes

No

Standard

Assessed

C

3.1CE

Find critical points and extreme values (max/min) of functions by using derivatives.

Question

Find all critical points and local maximums and minimums of the function. Show your work.

f(x)=x3+5x2−9x−45

[Solution here]

Standard

Assessed

E

3.2RM

Graphically and using derivatives, find the values guaranteed to exist by Rolle’s Theorem and by the Mean Value Theorem.

Question

Consider the function

f(x)=x3+5x2−9x−45 on the interval

[−5,3]

.

  1. Verify that the hypotheses of the Mean Value Theorem are satisfied for this function on the given interval.
  2. Find the value of a number “c” which the Mean Value Theorem guarantees.

[Solution here]

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Daniel Kevins

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