4) Find a formula for the line tangent to the curve at the point (4,4).

Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter58: Achievement Review—section Five
Section: Chapter Questions
Problem 30AR: Determine dimension x to 3 decimal places.
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4

Consider the curve with equation
(**)
+ tan
In
= evy
x + y
(Note that the first term is e raised to the power
4
1)
Check (algebraically) that the point (4, 4) lies on this curve.
dy
2)
Find
using implicit differentiation.
dx
Transcribed Image Text:Consider the curve with equation (**) + tan In = evy x + y (Note that the first term is e raised to the power 4 1) Check (algebraically) that the point (4, 4) lies on this curve. dy 2) Find using implicit differentiation. dx
[dy'
Find the value of
dx
(4,4)
3)
4)
Find a formula for the line tangent to the curve at the point (4,4).
5)
Suppose that f is the function implicitly defined by the equation
x + y
()
+ tan ( In
ev
near the point (4,4). Then, in a very small interval I containing 4, is f an increasing function or a
decreasing function? Explain your answer based on your work from above.
Transcribed Image Text:[dy' Find the value of dx (4,4) 3) 4) Find a formula for the line tangent to the curve at the point (4,4). 5) Suppose that f is the function implicitly defined by the equation x + y () + tan ( In ev near the point (4,4). Then, in a very small interval I containing 4, is f an increasing function or a decreasing function? Explain your answer based on your work from above.
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ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,