Unit 5 Review

Which of the following is a required condition for the Mean Value Theorem?

• f(x) is differentiable on [a, b]

• f(x) is continuous on [a, b]

• f(a) = f(b)

• f'(x) = 0

What is the conclusion of the Mean Value Theorem?

• at some point f'(x) = 0

• f(x) has an average value

• average rate = instant rate

• all values between f(a) and f(b) are represented

y has a relative minimum when

• y changes from + to -

• y' changes from - to +

• y' = 0

• y' changes from + to -

If   $x=0.5$  is a critical point of  $f\left(x\right)$  and  $f''\left(x\right)\ =\ \cos^2x\cdot\ln x$  then  $x=0.5$  is a 

• local maximum

• local minimum

• neither

Tags

CCSS.HSF.IF.C.7

Let f be the function given by f(x) = x³.  What are all values of c that satisfy the conclusion of the Mean Value Theorem on the closed interval [-1, 2]?  (No calculator)

• 0 only
• 1 only
• √3 only
• -1 and 1

The following sign chart shows whether  $f'\left(x\right)$  is positive, negative, or zero.
There is/are ...

• a local maximum at   $x=-2$  

• a local maximum at  $x=4$  

• local maxima at  $x=-2$  and  $x=4$  

• no local extrema

Where does the function, f(x) = 2x³ - 9x² + 12x -3 have relative max/min values?

• Rel max x = -1, Rel min x = 2

• Rel min x = 1, Rel min x = 2

• Rel max x = 1, Rel min x = 2

• Rel max x = 2, Rel min x = 1

Let f be the function with derivative given by f'(x) = x² - 2/x. On which of the following intervals is f decreasing?

• (-∞, 0]

• (-1, 0]

• (0, ∛2]

• (∛2, ∞)

Given a function, f(x), if f'(x)>0 over a certain interval, then f(x) is __________ over that interval.

• increasing
• decreasing
• concave up
• concave down

Given a function g(x), if g'(x)=0 at a certain value of x, then g(x) has _____________ at x.

• an inflection point
• a critical point
• a minimum
• a maximum