Questions from College Mathematics

Q: (A) Find  = (x). (B

(A) Find  = (x). (B) Find the slopes of the lines tangent to the graph of  at x = 0, 2, and 4. (C) Graph  and sketch in the tangent lines at x = 0, 2, and 4.  (x) = 4x - x2 + 1

Q: Repeat Problem 59 with (x) = 8x2 - 4x.

Repeat Problem 59 with (x) = 8x2 - 4x. Data from Problem 59: If an object moves along a line so that it is at y = (x) = 4x2 - 2x at time x (in seconds), find the instantaneous velocity function v...

Q: Let (x) = -x2 , g(x)

Let (x) = -x2 , g(x) = -x2 - 1, and h(x) = -x2 + 2. (A) How are the graphs of these functions related? How would you expect the derivatives of these functions to be related? (B) Use the four-step...

Q: Discuss the validity of each statement. If the statement is always

Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If (x) = mx + b is a linear function, then ’(x) = m.

Q: Discuss the validity of each statement. If the statement is always

Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. if a function f is differentiable on the interval (a, b), then f is continuous on (...

Q: Refer to the description of a standard deck of 52 cards and

Refer to the description of a standard deck of 52 cards and Figure 4 on page 384. An experiment consists of dealing 5 cards from a standard 52-card deck. In Problems what is the probability of being...

Q: Discuss the validity of each statement. If the statement is always

Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If the graph of f has a sharp corner at x = a, then f is not continuous at x = a

Q: sketch the graph of  and determine where  is nondifferentiable.

sketch the graph of  and determine where  is nondifferentiable.

Q: sketch the graph of  and determine where  is nondifferentiable.

sketch the graph of  and determine where  is nondifferentiable.

Q: Determine whether  is differentiable at x = 0 by considering

Determine whether  is differentiable at x = 0 by considering (x) = 1 - | x |