Test Review and Riemann Sum approximation

• -1
• 1
• 0
• 12

• pi
• -1
• 1
• -pi

Tags

CCSS.HSF.IF.A.2

• 0
• 5/3
• e^5x
• DNE

For which theorem must the function be continuous over [a, b]?

• EVT

• MVT

• Both EVT & MVT

• Neither EVT or MVT

For which theorem does it NOT matter that the function be differentiable over (a, b)?

• Both EVT & MVT

• MVT

• EVT

• Neither EVT or MVT

After finding a critical point, how do I determine the y-value of the point?

• Plug it in to f'(x)

• Plug it in to f(x)

• Nothing. I am done.

• It is always a max

The Mean Value Theorem applies to f(x) = 3x - x² on the interval [2, 5].

Find the value of x that satisfies the mean value theorem.

• 2.5

• 4

• 3.5

• -2

Use the sign chart for f'(x).
There is(are) ...

• a local maximum at x = -2.
• a local maximum at x = 4.
• local maxima at x = -2 and x = 4.
• no extrema.

Over what intervals is f(x) decreasing?

• (-∞, -1) ∪ (1, ∞)
• (-∞, -√3) ∪ (0, √3)
• (-1, 1)
• (-√3, 0) ∪ (√3, ∞)

If f'(x) = 0 what does that imply about the x value?

• It is a critical point, it is a possible max, min, or point of inflection.

• That the limit does not exist.