Question

Sketch the graph of a function that satisfies the given criteria.

f(1) = 0, f^ prime (-1)=f^ prime (2)=f^ prime (10)=0 lim x
infty f(x)=1 lim x 6 f(x)=- infty f^ prime (x)<0 ort(-
infty,-1),(2,7),(10, infty) f^ prime (x)>0 on(-1,2),(7,10) f^
prime prime (x)>0 on(- infty,1),(13, infty) f^ prime prime
(x)<0 on (1,7),(7,13)

Answer #1

When x= 1; y = 0

There is a horizontal tangents at x = -1, 2, 10

There is a horizontal asymptote at y = 1.

There is a vertical asymptote at x = 7.

The function decreases at the given intervals.

The function increases for the given intervals.

At the given interval the function is concave up.

The function is concave down in this interval.

7. (a) Sketch a graph of a function f(x) that satisfies all of
the following conditions.
i. f(2) = 3 and f(1) = −1
ii. lim x→−4 f(x) = −∞
iii. limx→∞ f(x) = 1
iv. lim x→−∞ f(x) = −2
v. lim x→−1+ f(x) = ∞
vi. lim x→−1− f(x) = −∞
vii. f 0 (x) > 0 on (−4, −3.5) ∪ (−2.5, −1.5) ∪ (1, 2) ∪ (2,
∞)
viii. f 0 (x) < 0 on (−∞, −4)...

Sketch a graph of a function that satisfies the following
conditions. Then take a picture and upload your graph.
f is continuous and even
f(2) = -1
f'(x) = 2x if 0 < x < 2
f'(x) = -2/3 if 2 < x < 5
f'(x) = 0 if x > 5

sketch the graph of one and only one function that satisfies all
the conditions listed below:
a. f(-x) = -f(x)
b. lim as x approaches 4- f(x)= infinity
c.lim as x approaches 4+ f(x)=-infinity
d. Limit as x approaches infinity f(x)=2
e. the second derivative of f(x) >0 on the interval (0,4)

Sketch the graph of a function f(x) that satisfies all of the
conditions listed below. Be sure to clearly label the axes.
f(x) is continuous and differentiable on its entire domain,
which is (−5,∞)
limx→-5^+ f(x)=∞
limx→∞f(x)=0limx→∞f(x)=0
f(−2)=−4,f′(−2)=0f(−2)=−4,f′(−2)=0
f′′(x)>0f″(x)>0 for −5<x<1−5<x<1
f′′(x)<0f″(x)<0 for x>1x>1

Sketch a continuous graph that satisfies each set of
conditions.
d) f"(x)=1 when x>-2, f"(x)=-1 when x<-2, f(-2)=-4

Given f(x)= x3-x2; [-1,2] answer the
following questions. a) Find the value(s) of c that satisfies the
Mean Value Theorem. b) Graph the function and explain what your
solutions in part (a) represent.

Curve Sketching Practice
Use the information to the side to sketch the graph of
f.
Label any asymptotes, local extrema, and inflection
points.
f is a polynomial function
x
—1
—6
3
—2
6
5
f is a polynomial function
x
1
—4
4
0
7
4

1) Verify that the function satisfies the three hypotheses of
Rolle's Theorem on the given interval. Then find all numbers c that
satisfy the conclusion of Rolle's Theorem. (Enter your answers as a
comma-separated list.)
f(x) = 1 − 12x + 2x^2, [2, 4]
c =
2) If f(2) = 7 and f '(x) ≥ 1 for 2 ≤
x ≤ 4, how small can f(4) possibly be?
3) Does the function satisfy the hypotheses of the Mean Value
Theorem...

Sketch a graph of a function having the following properties.
Make sure to label local extremes and inflection points.
1) f is increasing on (−∞, −2) and (3, 5) and decreasing on (−2,
0),(0, 3) and (5,∞).
2) f has a vertical asymptote at x = 0.
3) f approaches a value of 1 as x → ∞
4) f does not have a limit as x → −∞
5) f is concave up on (0, 4) and (8, ∞)...

Given that a function F is differentiable.
a
f(a)
f1(a)
0
0
2
1
2
4
2
0
4
Find 'a' such that limx-->a(f(x)/2(x−a)) = 2.
Provide with hypothesis and any results used.

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