Processor Speeds The processor speed, in megahertz (MHz), of Intel processors during the period 1996-2010 could be approximated by the following function of time t in years since the start of 1990: 53 v ( t ) = { 400 t − 2 , 200 if 6 ≤ t < 15 3 , 800 if 15 ≤ t ≤ 20 How fast and in what direction was processor speed changing in 2000?
Processor Speeds The processor speed, in megahertz (MHz), of Intel processors during the period 1996-2010 could be approximated by the following function of time t in years since the start of 1990: 53 v ( t ) = { 400 t − 2 , 200 if 6 ≤ t < 15 3 , 800 if 15 ≤ t ≤ 20 How fast and in what direction was processor speed changing in 2000?
Solution Summary: The author calculates the rate of change in processor speed in 2000 by using the first function as this value.
Processor Speeds The processor speed, in megahertz (MHz), of Intel processors during the period 1996-2010 could be approximated by the following function of time t in years since the start of 1990:53
v
(
t
)
=
{
400
t
−
2
,
200
if
6
≤
t
<
15
3
,
800
if
15
≤
t
≤
20
How fast and in what direction was processor speed changing in 2000?
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).
Does the series converge or diverge
Chapter 1 Solutions
Student Solutions Manual for Waner/Costenoble's Applied Calculus, 7th
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