Q: Show that the function f(x) =|x = 6
Show that the function f(x) =|x = 6| is not differentiable at 6. Find a formula for f’ and sketch its graph.
See AnswerQ: Where is the greatest integer function f(x) = [[
Where is the greatest integer function f(x) = [[x]] not differentiable? Find a formula for f’ and sketch its graph.
See AnswerQ: a. Sketch the graph of the function f(x)
a. Sketch the graph of the function f(x) = x|x|. b. For what values of x is f differentiable? c. Find a formula for f’.
See AnswerQ: a. Sketch the graph of the function g(x)
a. Sketch the graph of the function g(x) = x +|x|. b. For what values of x is g differentiable? c. Find a formula for g’.
See AnswerQ: Recall that a function f is called even if f(-x
Recall that a function f is called even if f(-x) = f(x) for all x in its domain and odd if f(-x) = -f(x) for all such x. Prove each of the following. a. The derivative of an even function is an odd f...
See AnswerQ: The left-hand and right-hand derivatives off at a
The left-hand and right-hand derivatives off at a are defined by if these limits exist. Then f’(a) exists if and only if these one-sided derivatives exist and are equal. a. Find f...
See AnswerQ: Nick starts jogging and runs faster and faster for 3 minutes,
Nick starts jogging and runs faster and faster for 3 minutes, then he walks for 5 minutes. He stops at an intersection for 2 minutes, runs fairly quickly for 5 minutes, then walks for 4 minutes. a....
See AnswerQ: When you turn on a hot-water faucet, the temperature
When you turn on a hot-water faucet, the temperature T of the water depends on how long the water has been running. a. Sketch a possible graph of T as a function of the time t that has elapsed since...
See AnswerQ: Determine / a. by evaluating f(
Determine a. by evaluating f(x) = 1/(x3 – 1) for values of x that approach 1 from the left and from the right, b. by reasoning as in Example 9, and c. from a graph of f.
See AnswerQ: Let ℓ be the tangent line to the parabola y = x2
Let ℓ be the tangent line to the parabola y = x2 at the point (1, 1). The angle of inclination of l is the angle ϕ that ℓ makes with the positive direction of the x-axis. Calculate ϕ correct to the...
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