(e) Assuming that f(0) = 0, sketch a graph of f.yy54mum321X7654321y-2-322446688X-3-4-622446688Xi The graph of the derivative f' of a continuous function f is shown. (Assume f' continues to ∞.)yX =4y = f'(x)Vi2X =-2--2i(a) On what interval(s) is f increasing? (Enter your answer in interval notation.)18On what interval(s) is f decreasing? (Enter your answer in interval notation.)X(b) At what value(s) of x does f have a local maximum? (Enter your answers as a comma-separated list.)X =At what value(s) of x does f have a local minimum? (Enter your answers as a comma-separated list.)(c) On what interval(s) is f concave upward? (Enter your answer in interval notation.)On what interval(s) is f concave downward? (Enter your answer in interval notation.)(d) State the x-coordinate(s) of the point(s) of inflection. (Enter your answers as a comma-separated list.)

Answered: The graph of the derivative f' of a…

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter1: Functions

Section1.2: Functions Given By Tables

Problem 32SBE: Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it...

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Question

(e) Assuming that f(0) = 0, sketch a graph of f.
y
y
5
4
mum
3
2
1
X
7
6
5
4
3
2
1
y
-2
-3
2
2
4
4
6
6
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8
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-3
-4
-6
2
2
4
4
6
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i

The graph of the derivative f' of a continuous function f is shown. (Assume f' continues to ∞.)
y
X =
4
y = f'(x)
Vi
2
X =
-2-
-2
i
(a) On what interval(s) is f increasing? (Enter your answer in interval notation.)
18
On what interval(s) is f decreasing? (Enter your answer in interval notation.)
X
(b) At what value(s) of x does f have a local maximum? (Enter your answers as a comma-separated list.)
X =
At what value(s) of x does f have a local minimum? (Enter your answers as a comma-separated list.)
(c) On what interval(s) is f concave upward? (Enter your answer in interval notation.)
On what interval(s) is f concave downward? (Enter your answer in interval notation.)
(d) State the x-coordinate(s) of the point(s) of inflection. (Enter your answers as a comma-separated list.)

Expert Solution

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$A c c o r d i n g t o o u r g u i d e l i n e s w e c a n s o l v e f i r s t f o u r s u b p a r t p l e a s e a s k r e m a i n i n g a g a i n . s o l u t i o n : - (a) f' (x) > 0, x \in (0, 2) \cup (4, 6) \cup (8, \infty), f (x) i s i n c r e a \sin g f' (x) < 0, x \in (2, 4) \cup (6, 8), f (x) i s d e c r e a \sin g (b) f (x) h a s l o c a l m a x i m u m a t x = 0 f (x) h a s l o c a l m i n i m u m a t x = 3 (c) f'' (x) > 0, x \in (3, 6) \cup (6, \infty), f (x) i s c o n c a v e u p w a r d f'' (x) < 0, x \in (0, 3) f (x) i s c o n c a v e d o w n w a r d$