f'(1) 4. Given to the right is the graph of f'(z), the DERIVATIVE of a function f(z). Use this graph to answer the following questions, estimating as accurately as possible from the graph. 41 3 2 (a) On what interval(s) is f(z) decreasing? Briefly explain how you chose your interval(s). (b) On what interval(s) is f(x) concave up? Briefly explain how you chose your interval(s). (c) List all places where f(x) has a local minimum value. Briefly explain how you chose your answer(s). (d) List all places where f'(z) has a local minimum value.
f'(1) 4. Given to the right is the graph of f'(z), the DERIVATIVE of a function f(z). Use this graph to answer the following questions, estimating as accurately as possible from the graph. 41 3 2 (a) On what interval(s) is f(z) decreasing? Briefly explain how you chose your interval(s). (b) On what interval(s) is f(x) concave up? Briefly explain how you chose your interval(s). (c) List all places where f(x) has a local minimum value. Briefly explain how you chose your answer(s). (d) List all places where f'(z) has a local minimum value.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:f'(x)
4. Given to the right is the graph of f'(r), the DERIVATIVE of a
function f(z). Use this graph to answer the following questions,
estimating as accurately as possible from the graph.
41
3
1
(a) On what interval(s) is f(x) decreasing? Briefly explain how
you chose your interval(s).
(b) On what interval(s) is f(r) concave up? Briefly explain how you chose your interval(s).
(c) List all places where f(r) has a local minimum value. Briefly explain how you chose your answer(s).
(d) List all places where f'(x) has a local minimum value.
Expert Solution
a) answer
When the slope of the tangents is negative then the function is said to be decreasing.
Find the intervals of the given graph in which the derivative function is negative.
Such intervals are:
b) answer
A function is said to be concave up, when the sign of the derivative function changes from negative to positive.
From the given graph of the derivative function, the function changes its sign from negative to positive in the intervals:
Therefore, in these two intervals the function is concave upwards.
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