Questions from General Calculus

Q: Suppose that f (t) = t2 + 3t -

Suppose that f (t) = t2 + 3t - 7. (a) What is the average rate of change of f (t) over the interval 5 to 6? (b) What is the (instantaneous) rate of change of f (t) when t = 5?

Q: Suppose that f (t) = 3t + 2 – 12

Suppose that f (t) = 3t + 2 – 12/t. (a) What is the average rate of change of f (t) over the interval 2 to 3? (b) What is the (instantaneous) rate of change of f (t) when t = 2?

Q: An object moving in a straight line travels s(t)

An object moving in a straight line travels s(t) kilometers in t hours, where s(t) = 2t2 + 4t. (a) What is the object’s velocity when t = 6? (b) How far has the object traveled in 6 hours? (c) When is...

Q: After an advertising campaign, the sales of a product often increase

After an advertising campaign, the sales of a product often increase and then decrease. Suppose that t days after the end of the advertising, the daily sales are f (t) = -3t2 + 32t + 100 units. What i...

Q: An analysis of the daily output of a factory assembly line shows

An analysis of the daily output of a factory assembly line shows that about 60t + t2 – 1/12 t3 units are produced after t hours of work, 0 ≤ t ≤ 8. What is the rate of production (in units per hour) w...

Q: Liquid is pouring into a large vat. After t hours,

Liquid is pouring into a large vat. After t hours, there are 5t + √t gallons in the vat. At what rate is the liquid flowing into the vat (in gallons per hour) when t = 4?

Q: Maximum height A toy rocket is fired straight up into the air

Maximum height A toy rocket is fired straight up into the air. Let s(t) = -6t2 + 72t denote its position in feet after t seconds. (a) Find the velocity after t seconds. (b) Find the acceleration after...

Q: Differentiate. y = (x2 + x)-2

Differentiate. y = (x2 + x)-2

Q: Refer to Fig. 6, where s(t) represents

Refer to Fig. 6, where s(t) represents the position of a car moving in a straight line. (a) Was the car going faster at A or at B? (b) Is the velocity increasing or decreasing at B? What does this say...

Q: A toy rocket fired straight up into the air has height s

A toy rocket fired straight up into the air has height s(t) = 160t - 16t2 feet after t seconds. (a) What is the rocket’s initial velocity (when t = 0)? (b) What is the velocity after 2 seconds? (c) Wh...