The formula t = 1 c ln ( A A − N ) describes the lime, t , in weeks, that it takes to achieve mastery of a portion of a task. In the formula, A represents maximum learning possible, N is the portion of the learning that is to be achieved, and c is a constant used to measure an individual’s learning style. A 50-year-old man decides to start running as a way to maintain good health. He feels that the maximum rate he could ever hope to achieve is 12 miles per hour. How many weeks will it take before the man can run 5 miles per hour if c = 0 ⋅ 06 for this person?
The formula t = 1 c ln ( A A − N ) describes the lime, t , in weeks, that it takes to achieve mastery of a portion of a task. In the formula, A represents maximum learning possible, N is the portion of the learning that is to be achieved, and c is a constant used to measure an individual’s learning style. A 50-year-old man decides to start running as a way to maintain good health. He feels that the maximum rate he could ever hope to achieve is 12 miles per hour. How many weeks will it take before the man can run 5 miles per hour if c = 0 ⋅ 06 for this person?
Solution Summary: The author calculates the number of weeks it would take for the man to run 5 miles an hour. Substitute the values in above equation and simplify as follows.
describes the lime, t, in weeks, that it takes to achieve mastery of a portion of a task. In the formula, A represents maximum learning possible, N is the portion of the learning that is to be achieved, and c is a constant used to measure an individual’s learning style. A 50-year-old man decides to start running as a way to maintain good health. He feels that the maximum rate he could ever hope to achieve is 12 miles per hour. How many weeks will it take before the man can run 5 miles per hour if
c
=
0
⋅
06
for this person?
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5)
=
4.
-
3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
and f'(2).
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.