1. (#11 Exam 1 Review) Find the equation of the line tangent to the graph of the function: f(x) = x-2x² at x = 1. You must use the Definition of the Derivative to obtain the derivative. 2. (#9 Exam 1 Review) Sketch the graph of the function g for which: g(0) = g(2) = g(4) = 0, g' (1) = g(3)=0,g (2)=-1, lim g(x) = ∞o, and lim g(x) = -∞ z-5 2--1+
1. (#11 Exam 1 Review) Find the equation of the line tangent to the graph of the function: f(x) = x-2x² at x = 1. You must use the Definition of the Derivative to obtain the derivative. 2. (#9 Exam 1 Review) Sketch the graph of the function g for which: g(0) = g(2) = g(4) = 0, g' (1) = g(3)=0,g (2)=-1, lim g(x) = ∞o, and lim g(x) = -∞ z-5 2--1+
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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Transcribed Image Text:1. (#11 Exam 1 Review) Find the equation of the line tangent to the graph of the function: f (x) = x-2x² at x = 1. You must use the Definition of the Derivative to obtain the
derivative.
2. (#9 Exam 1 Review) Sketch the graph of the function g for which:
g(0) = g(2) = g(4) = 0, g' (1) = g(3) = 0,g' (2) = -1, lim g(x) = ∞, and lim g(x) = -∞
x 5
x-1+
3. State the three-part Definition of Continuity.
4. (#13 Exam 1 Review) The graph of f is given. State, with mathematically correct reasons, the values for which f is not differentiable.
-2
VA
0
2
4 X
(Description: Graph with three components. First component is horizontal line in the 2nd quadrant to x = -2. Sharp turn upwards in downward arc into the 1st quadrant and ends with
open dot where x = 1. Second component is solid dot at x = 1 vertically below the open dot. Third component begins with open dot at x = 1 below the solid dot. The graph falls in
downward arc shape into the 4th quadrant, takes a sharp turn at x = 3 and continues as horizontal line.)
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