consider the function f(x) = 12(x-1)^-2 find the value c such that the triangle formed by the tangent line to f at c and the axes has the largest possible area c=______________________ find the maximum area of the triangle formed by the tangent line to f at c and the axes A=_______________________________units^2
consider the function f(x) = 12(x-1)^-2 find the value c such that the triangle formed by the tangent line to f at c and the axes has the largest possible area c=______________________ find the maximum area of the triangle formed by the tangent line to f at c and the axes A=_______________________________units^2
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 15T
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Question
consider the function f(x) = 12(x-1)^-2
find the value c such that the triangle formed by the tangent line to f at c and the axes has the largest possible area
c=______________________
find the maximum area of the triangle formed by the tangent line to f at c and the axes
A=_______________________________units^2
Expert Solution
Step 1
Equation of tangent is:
Step 2
Point wherein the tangent will touch x-axis is y=0 or:
Step 3
Point wherein the tangent will touch y-axis is x=0 or:
Step 4
Thus area of triangle is or or .
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