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.
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 5×2−9x−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 5×2−9x−45 on the interval [−5,3]
. Verify that the hypotheses of the Mean Value Theorem are satisfied for this function on the given interval.
Find the value of a number “c” which the Mean Value Theorem guarantees.
[Solution here]