Questions from General Calculus

Q: In an 8-second test run, a vehicle accelerates for

In an 8-second test run, a vehicle accelerates for several seconds and then decelerates. The function s(t) gives the number of feet traveled after t seconds and is graphed in Fig. 9. (a) How far has t...

Q: In a psychology experiment, people improved their ability to recognize common

In a psychology experiment, people improved their ability to recognize common verbal and semantic information with practice. Their judgment time after t days of practice was f (t) = .36 + .77(t - .5)-...

Q: A ball thrown straight up into the air has height s(

A ball thrown straight up into the air has height s(t) = 102t - 16t2 feet after t seconds. (a) Display the graphs of s(t) and s’(t) in the window [0, 7] by [-100, 200]. Use these graphs to answer the...

Q: If f (x) = x2 + 3x, calculate the

If f (x) = x2 + 3x, calculate the average rate of change of f (x) over the following intervals (a) 1 …≤ x ≤ 2, (b) 1 ≤ x ≤ 1.5, (c) 1 ≤ x ≤ 1.1.

Q: If f (x) = 3x2 + 2, calculate the

If f (x) = 3x2 + 2, calculate the average rate of change of f (x) over the following intervals (a) 0 ≤ x ≤ .5, (b) 0 ≤ x ≤ .1, (c) 0 ≤ x ≤ .0.01.

Q: Suppose that f (x) = 4x2. (a

Suppose that f (x) = 4x2. (a) What is the average rate of change of f (x) over each of the intervals 1 to 2, 1 to 1.5, and 1 to 1.1? (b) What is the (instantaneous) rate of change of f (x) when x = 1?...

Q: Give a physical description of what is meant by the slope of

Give a physical description of what is meant by the slope of f (x) at the point (2, f (2)).

Q: What does f ‘(2) represent?

What does f ‘(2) represent?

Q: Explain why the derivative of a constant function is 0.

Explain why the derivative of a constant function is 0.

Q: State the power rule, the constant-multiple rule, and

State the power rule, the constant-multiple rule, and the sum rule, and give an example of each.