Questions from General Calculus

Q: The figure shows the graph of the derivative f' of a function

The figure shows the graph of the derivative f' of a function f. (a). Sketch the graph of f". (b). Sketch a possible graph of f.

Q: (a). Find equations of both lines through the point (

(a). Find equations of both lines through the point (2, -3) that are tangent to the parabola y = x2 + x. (b). Show that there is no line through the point (2, 7) that is tangent to the parabola. Then...

Q: Sketch the graph of a function that satisfies the given conditions:

Sketch the graph of a function that satisfies the given conditions:

Q: Find equations of the tangent line and normal line to the curve

Find equations of the tangent line and normal line to the curve at the given point. x2 + 4xy + y2 = 13, (2, 1)

Q: Find the limit. limv→14+ 4 – v

Find the limit. limv→14+ 4 – v/|4 – v|

Q: Find the limit. limu→1 u4 – 1/

Find the limit. limu→1 u4 – 1/u3 + 5u2 – 6u

Q: If f (x) =xesin x, find f'(

If f (x) =xesin x, find f'(x). Graph f and f' on the same screen and comment.

Q: (a). Graph the function f (x) = x

(a). Graph the function f (x) = x – 2 sin x in the viewing rectangle [0, 8] by [-2, 8]. (b). On which interval is the average rate of change larger: [1, 2] 0r [2, 3]. (c). At which value of is the ins...

Q: Suppose that h (x) f (x) g (

Suppose that h (x) f (x) g (x) and F (x) = f (g (x)), where f (2) = 3, g (2) = 5, g'(2) = 4, f'(2) = -2, and f'(5) = 11. Find (a) h'(2) and (b) F'(2).

Q: If f and g are the functions whose graphs are shown,

If f and g are the functions whose graphs are shown, let P (x) = f (x) g (x), Q (x) = f (x)/g (x), and C (x) = f (g (x)). Find (a) P'(2), (b) Q'(2), and (c) C'(2).