Questions from General Calculus

Q: In an episode of The Simpsons television show, Homer reads from

In an episode of The Simpsons television show, Homer reads from a newspaper and announces “Here’s good news! According to this eye-catching article, SAT scores are declining at a slower rate.” Interpr...

Q: The president announces that the national deficit is increasing, but at

The president announces that the national deficit is increasing, but at a decreasing rate. Interpret this statement in terms of a function and its first and second derivatives.

Q: Let f (t) be the temperature at time t where

Let f (t) be the temperature at time t where you live and suppose that at time t = 3 you feel uncomfortably hot. How do you feel about the given data in each case? (a) f ‘(3) = 2, f ‘(3) = 4 (b) f ‘(3...

Q: Two curves are orthogonal if their tangent lines are perpendicular at each

Two curves are orthogonal if their tangent lines are perpendicular at each point of intersection. Show that the given families of curves are orthogonal trajectories of each other; that is, every curve...

Q: Let K(t) be a measure of the knowledge you

Let K(t) be a measure of the knowledge you gain by studying for a test for t hours. Which do you think is larger, K(8) – K(7) or K(3) – K(2)? Is the graph of K concave upward or concave downward? Why?...

Q: Coffee is being poured into the mug shown in the figure at

Coffee is being poured into the mug shown in the figure at a constant rate (measured in volume per unit time). Sketch a rough graph of the depth of the coffee in the mug as a function of time. Account...

Q: (a) Find the critical numbers of f (x)

(a) Find the critical numbers of f (x) = x4(x – 1)3. (b) What does the Second Derivative Test tell you about the behavior of f at these critical numbers? (c) What does the First Derivative Test tell y...

Q: A drug response curve describes the level of medication in the bloodstream

A drug response curve describes the level of medication in the bloodstream after a drug is administered. A surge function S(t) = Atpe-kt is often used to model the response curve, reflecting an initia...

Q: Find a cubic function f (x) = ax3 + bx2

Find a cubic function f (x) = ax3 + bx2 + cx + d that has a local maximum value of 3 at x = -2 and a local minimum value of 0 at x = 1.

Q: (a) If the function f (x) = x3

(a) If the function f (x) = x3 + ax2 + bx has the local minimum value − 2 9 3 at x = 1/ 3 , what are the values of a and b? (b) Which of the tangent lines to the curve in part (a) has the smallest...