The tangent line to the graph of f(x) at x = 1 is shown. On the tangent line, P is the point of tangency and A is another point on the line.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
The tangent line to the graph of f(x) at x = 1 is shown. On the tangent line, P is the point of tangency and A is another point on
the line.
-3
A(x, y) =
y = f(x)
2
y
(c) Find f'(1).
-1
-2
1
(a) Find the coordinates of the points P and A.
P(x, y) =
2
3
X
(b) Use the coordinates of P and A to find the slope of the tangent line.
(d) Find the instantaneous rate of change of f(x) at P.
e
Transcribed Image Text:The tangent line to the graph of f(x) at x = 1 is shown. On the tangent line, P is the point of tangency and A is another point on the line. -3 A(x, y) = y = f(x) 2 y (c) Find f'(1). -1 -2 1 (a) Find the coordinates of the points P and A. P(x, y) = 2 3 X (b) Use the coordinates of P and A to find the slope of the tangent line. (d) Find the instantaneous rate of change of f(x) at P. e
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