Slope of Line PQ -5 Slope of Line PQ Q (-1, 1) (-2, 6) = -5 (-1, 1) (0, ) 1 (-1, 1) (-1.5, 3.25) (-1, 1) (-0.5, (-1, 1) (-1.1, ) (-1, 1) (-0.9, (-1, 1) (-1.01, ) (-1, 1) (-0.99, ) (-1, 1) (-1.001, ) (-1, 1) (-0.999, b) Use your results for part a to approximate the slope of the tangent to the graph of f(x) at a point P c) Calculate the slope of the secant where the x- coordinate of Q is -1 + h

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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Part 1: Consider the function y = x²- 2x -2
a) Copy and complete the following tables of values. P and Q are points on the graph of
f(x)
Slope of
Line PQ
Slope of
Line PQ
P
(-1, 1)
(-2, 6)
= -5
(-1, 1)
(0, )
(-1, 1) (-1.5, 3.25)
(-1, 1)
(-0.5,
(-1, 1) (-1.1,
(-1, 1)
(-0.9,
(-1, 1) (-1,01, )
(-1, 1) (-0.99,
(-1, 1) (-1.001,
(-1, 1) (-0.999, )
b) Use your results for part a to approximate the slope of the tangent to the graph of f(x) at
a point P
c) Calculate the slope of the secant where the x- coordinate of Q is -1 + h
d) Use your results for part c to calculate the slope of the tangent to the graph of f(x) at
point P.
e) Compare your answers for parts b and d.
Transcribed Image Text:Part 1: Consider the function y = x²- 2x -2 a) Copy and complete the following tables of values. P and Q are points on the graph of f(x) Slope of Line PQ Slope of Line PQ P (-1, 1) (-2, 6) = -5 (-1, 1) (0, ) (-1, 1) (-1.5, 3.25) (-1, 1) (-0.5, (-1, 1) (-1.1, (-1, 1) (-0.9, (-1, 1) (-1,01, ) (-1, 1) (-0.99, (-1, 1) (-1.001, (-1, 1) (-0.999, ) b) Use your results for part a to approximate the slope of the tangent to the graph of f(x) at a point P c) Calculate the slope of the secant where the x- coordinate of Q is -1 + h d) Use your results for part c to calculate the slope of the tangent to the graph of f(x) at point P. e) Compare your answers for parts b and d.
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