For Exercises 111-114, use the graph of y = f x to answer the following. (See Example 10) a . Determine f − 2 . b . Determine f 3 . c . Find all x for which f x = − 1. d . Find all x for which f x = − 4. e . Determine the x -intercept s . f . Determine the y -intercept . g . Determine the domain of f . h . Determine the range of f
For Exercises 111-114, use the graph of y = f x to answer the following. (See Example 10) a . Determine f − 2 . b . Determine f 3 . c . Find all x for which f x = − 1. d . Find all x for which f x = − 4. e . Determine the x -intercept s . f . Determine the y -intercept . g . Determine the domain of f . h . Determine the range of f
For Exercises 111-114, use the graph of
y
=
f
x
to answer the following. (See Example 10)
a
. Determine
f
−
2
.
b
. Determine
f
3
.
c
. Find all
x
for which
f
x
=
−
1.
d
. Find all
x
for which
f
x
=
−
4.
e
. Determine the
x
-intercept
s
.
f
. Determine the
y
-intercept
.
g
. Determine the domain of
f
.
h
. Determine the range of
f
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).
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