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Consider the function f(x) = 2-e on [-1,1], and a point a € [-1,1]. Consider the triangle formed by the tangent line to f at a, and the lines z = 0 and y= 0. Find the points a such that the triangle has an area of exactly 4/e. If necessary, approximate the value a to 3 places after the decimal.

Consider the function f(x) = 2-e on [-1,1], and a point a € [-1,1]. Consider the triangle formed by the tangent line to f at a, and the lines z = 0 and y= 0. Find the points a such that the triangle has an area of exactly 4/e. If necessary, approximate the value a to 3 places after the decimal.

Advanced Engineering Mathematics
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 1. Differentiation 1. Consider the function f(x)= 2-e on [-1,1], and a point a € [-1,1]. Consider the triangle formed by the tangent line to f at a, and the lines z= 0 and y=0. Find the points a such that the triangle has an area of exactly 4/e. If necessary, approximate the value a to 3 places after the decimal. 2. Suppose that the tangent line to the graph of f(x) = (6) at r= 1 is equal to the tangent line to the graph of g(x) = 2ln(e2+e-2²)-2 ln(2)-1 at z=0. What is the value of the positive constant b, and what is the equation of the tangent line?
Transcribed Image Text:Question 1. Differentiation 1. Consider the function f(x)= 2-e on [-1,1], and a point a € [-1,1]. Consider the triangle formed by the tangent line to f at a, and the lines z= 0 and y=0. Find the points a such that the triangle has an area of exactly 4/e. If necessary, approximate the value a to 3 places after the decimal. 2. Suppose that the tangent line to the graph of f(x) = (6) at r= 1 is equal to the tangent line to the graph of g(x) = 2ln(e2+e-2²)-2 ln(2)-1 at z=0. What is the value of the positive constant b, and what is the equation of the tangent line?
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