L P A y=x Q >x Consider the function ƒ defined by f(x) = 90e−0.5x for x Є R+. The graph of ƒ and the line y = x intersect at point P. (a) Find the x-coordinate of P. The line I has a gradient of -1 and is a tangent to the graph of ƒ at the point Q. (b) Find the exact coordinates of Q. (c) Show that the equation of L is y = −x + 2ln 45 +2. The shaded region A is enclosed by the graph of ƒ and the lines y = x and L.
L P A y=x Q >x Consider the function ƒ defined by f(x) = 90e−0.5x for x Є R+. The graph of ƒ and the line y = x intersect at point P. (a) Find the x-coordinate of P. The line I has a gradient of -1 and is a tangent to the graph of ƒ at the point Q. (b) Find the exact coordinates of Q. (c) Show that the equation of L is y = −x + 2ln 45 +2. The shaded region A is enclosed by the graph of ƒ and the lines y = x and L.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Transcribed Image Text:L
P
A
y=x
Q
>x
Transcribed Image Text:Consider the function ƒ defined by f(x) = 90e−0.5x for x Є R+.
The graph of ƒ and the line y = x intersect at point P.
(a) Find the x-coordinate of P.
The line I has a gradient of -1 and is a tangent to the graph of ƒ at the point Q.
(b) Find the exact coordinates of Q.
(c) Show that the equation of L is y = −x + 2ln 45 +2.
The shaded region A is enclosed by the graph of ƒ and the lines y = x and L.
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