18. Let f(x) = 18 /x - 3x. a. Find all points on the graph of f at which the tangent line is horizontal. b. Find all points on the graph of f at which the tangent line has slope - 2°
18. Let f(x) = 18 /x - 3x. a. Find all points on the graph of f at which the tangent line is horizontal. b. Find all points on the graph of f at which the tangent line has slope - 2°
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
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How do we do part b step by step?
Expert Solution
Step 1
Let
a. Let's find all points on the graph of at which the tangent line is horizontal.
For this purpose we derive and equal to zero.
So we have
Making we have
Evaluating at f we get
Then the point on the graph of where the tangent line is horizontal is
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