Optimization HW

• Intermediate Value Theorem (IVT)

• Extreme Value Theorem (EVT)

• Mean Value Theorem (MVT)

• IVT

• EVT

• MVT

• IVT

• EVT

• MVT

The value x=2 locates the

• Local or Relative maximum

• Local or relative minimum

• Global or Absolute Max

• Global or Absolute Min

• Local or Relative maximum

• Local or relative minimum

• Global or Absolute Max

• Global or Absolute Min

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

Which of the following is the absolute minimum point of the function y = x³+ 6x² -12 on the given interval [-2, 5]?

• (0, -12)

• (-4, 20)

• (-2, 4)

• (5, 263)

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

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation 
s(t) = –16t² + 64t + 80.
What will be the object's maximum height? 

• 2 ft
• 80 ft
• 144 ft
• 64 ft