Questions from General Calculus

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

Let f (t) be the temperature at time 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?

Q: (a). Sketch the graph of a function that has a

(a). Sketch the graph of a function that has a local maximum at 2 and is differentiable at 2. (b). Sketch the graph of a function that has a local maximum at 2 and is continuous but not differentiable...

Q: (a). Sketch the graph of a function on [-1

(a). Sketch the graph of a function on [-1, 2] that has an absolute maximum but no local maximum. (b). Sketch the graph of a function on [-1, 2] that has a local maximum but no absolute maximum.

Q: Sketch the graph of a function f that is continuous on [

Sketch the graph of a function f that is continuous on [1, 5] and has the given properties. Absolute minimum at 1, absolute maximum at 5, local maximum at 2, local minimum at 4

Q: Find the critical numbers of the function. f (x

Find the critical numbers of the function. f (x) = x3 + 6x2 - 15x

Q: (a). Find the intervals on which f is increasing or

(a). Find the intervals on which f is increasing or decreasing. (b). Find the local maximum and minimum values of f. (c). Find the intervals of concavity and the inflection points. f (x) = x2/x2 + 3

Q: Sketch the graph of a function f that is continuous on [

Sketch the graph of a function f that is continuous on [1, 5] and has the given properties. Absolute maximum at 5, absolute minimum at 2, local maximum at 3, local minima at 2 and 4

Q: Sketch the graph of a function f that is continuous on [

Sketch the graph of a function f that is continuous on [1, 5] and has the given properties. f has no local maximum or minimum, but 2 and 4 are critical numbers

Q: If a snowball melts so that its surface area decreases at a

If a snowball melts so that its surface area decreases at a rate of 1 cm2/min, find the rate at which the diameter decreases when the diameter is 10 cm. (a). What quantities are given in the problem?...

Q: Two carts, A and B, are connected by a rope

Two carts, A and B, are connected by a rope 39 ft long that passes over a pulley P (see the figure). The point Q is on the floor 12 ft directly beneath P and between the carts. Cart A is being pulled...