MVT, Relative Extrema, Inflection Points, and Optimization

The function, F, above satisfies the conclusion of Rolle's Theorem in the interval [a,b] because:

I. F is continuous

II. F is differentiable on (a,b)

III. F(a) = F(b) = 0

• All 3 statements are true

• Only 2 and 3 are true

• Only 1 is true

• None of the statements are true

What are inflection points in calculus?

• Inflection points are points where the curve intersects the x-axis

• Inflection points are points where the curve intersects the y-axis

• Inflection points are points where the curve is at its highest or lowest

• Inflection points in calculus are points on a curve where the concavity changes, indicating a change in the direction of the curve's curvature.

• 1

• 2

• 3/2

• 1/2

When looking for critical points we did....

• 1. took the limit of the function. 2. Graphed the critical points.
• 1. Found f'(x). 2. Set f'(x) = 0 and solved for x. 3. Created a sign diagram. 4. Took the limit
• 1. Found f'(x). 2. Set f'(x) = 0 and solved for x. 3. Created a sign diagram. 4. Checked out intervals.

• -1

• 5/3

• 3/5

• Rolle's Theorem doesn't apply

For what value of c is the Rolle's thm applicable on the given function f(x) = x²-5x+4 [1,4]

• c = 7/2

• c = 5/2

• c = 3/2

• c = 9/2

• c = 6

• c =7

• c = 5

• c = 3

What is the derivative of
f(x) = x² - 3x - 28 ?

• 2x - 3
• 2x + 3
• x - 3
• 2x² - 3x - 28

Select all that are true:

• The graph has an absolute minimum

• The graph has two relative extrema

• The graph has

  a relative minimum

  at x=1

• The graph is increasing on its domain.

What are the local minimums of the graph? Just enter numbers, separated by a comma: