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?

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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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):
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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