5. Below is a graph of the curve y = 4x 3 cos.x: 10T -10 10 -5 -10 Your friend claims that the slope of the tangent line to the curve at x = 4 is the negative of the slope of the tangent line to the curve at x = -4. Prove mathematically whether your friend is right or wrong. Is the slope of the tangent line to the curve at x = a the negative of the slope of the tangent line to the curve at x = -a for any other values of a? Explain.
5. Below is a graph of the curve y = 4x 3 cos.x: 10T -10 10 -5 -10 Your friend claims that the slope of the tangent line to the curve at x = 4 is the negative of the slope of the tangent line to the curve at x = -4. Prove mathematically whether your friend is right or wrong. Is the slope of the tangent line to the curve at x = a the negative of the slope of the tangent line to the curve at x = -a for any other values of a? Explain.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:5. Below is a graph of the curve y = 4x 3 cosx:
10T
-10
10
-10
Your friend claims that the slope of the tangent line to the curve at xr = 4 is the negative of the
slope of the tangent line to the curve at x = -4. Prove mathematically whether your friend is
right or wrong.
Is the slope of the tangent line to the curve at x = a the negative of the slope of the tangent line
to the curve at x = -a for any other values of a? Explain.
Transcribed Image Text:1+50 sinx:
(x²+3)
6. Below is a graph of the curve y =
10-
5t
-10
10
Looking at the graph, it's clear that the function has three zeros in the domain -5 <x< 5. Find
the three zeros, and find the slopes of the tangent lines to the curve at those x values.
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