compute the instantaneous slope at: (-4, 8) • Start with two points A : (-4,8) and B: (-4 + h, ?) What is the y-coordinate of B?
compute the instantaneous slope at: (-4, 8) • Start with two points A : (-4,8) and B: (-4 + h, ?) What is the y-coordinate of B?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![The instantaneous slope of f(x)
when f(x) is polynomial
10
1.0
1,0
F10
-10
f(x) = x² + x + 10
compute the instantaneous slope at: (-4, 8)
Start with two points
A : (-4, 8) and B : (-4 + h, ?)
What is the y-coordinate of B?
• Because the x-coordinate of B depends on h, the y-coordinate will also
depend on h.
Compute Ax and Ay
Compute and Reduce Ax/Ay
Finding the limit
Use the steps above to compute the instantaneous rate of change for f(x) at
(-4, 8), then use your answer to find an equation for the line tangent to f(x) at
(-4, 8):](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F198e67eb-75d1-437c-b039-7adea5064eee%2Fbf17754c-287f-42e3-bd8f-6c8bc45073df%2Fly32u4r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The instantaneous slope of f(x)
when f(x) is polynomial
10
1.0
1,0
F10
-10
f(x) = x² + x + 10
compute the instantaneous slope at: (-4, 8)
Start with two points
A : (-4, 8) and B : (-4 + h, ?)
What is the y-coordinate of B?
• Because the x-coordinate of B depends on h, the y-coordinate will also
depend on h.
Compute Ax and Ay
Compute and Reduce Ax/Ay
Finding the limit
Use the steps above to compute the instantaneous rate of change for f(x) at
(-4, 8), then use your answer to find an equation for the line tangent to f(x) at
(-4, 8):
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