Unit 5: Analytical Applications of Differentiation

If [math], at which [math]-value does [math] have a local maximum?

Let [math]. Using the second derivative test, classify the critical point.

Find the [math]-coordinate of the inflection point of [math].

Find the absolute maximum value of [math] on [math].

What is the absolute minimum value of [math] on [math]?

On which interval is [math] increasing?

A farmer has 200 feet of fencing to enclose a rectangular area along a river (no fence needed along the river). What is the maximum area in square feet?

The graph of [math], the derivative of [math], is shown above. On which interval does [math] have a local minimum?

If [math] and [math] for all [math] in an interval [math], which best describes the graph of [math] on [math]?

Let [math]. At which [math]-value does [math] have a local minimum?

The function [math] has [math] and [math]. What can be concluded about [math]?

On what interval is [math] concave up?

Find the absolute maximum value of [math] on [math].

How many inflection points does [math] have?

The graph of [math] is shown above. Which of the following is true about [math]?

If [math] is continuous on [math], differentiable on [math], and [math], which statement must be true?

Find the minimum value of the sum [math] for [math].

If [math], then [math] has a local maximum at [math] =

On what interval(s) is the graph of [math] concave up?

The absolute maximum value of [math] on [math] is