SOLUTION: f(x)=6x/x-2, determine the x coordinate of a point (x,y) where 3<x<5 and the slope of the tangent line at that point equals the slope of the secant line joining (3,18) and (5,10)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: f(x)=6x/x-2, determine the x coordinate of a point (x,y) where 3<x<5 and the slope of the tangent line at that point equals the slope of the secant line joining (3,18) and (5,10)      Log On


   

Question 398710: f(x)=6x/x-2, determine the x coordinate of a point (x,y) where 3
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=6x/x-2, determine the x coordinate of a point (x,y) where 3 ----
Slope of the secant = (18-10)/(3-5) = = -4
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f'(x) = [(x-2)*6-(6x)(1)]/(x-2)^2
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Solve f'(x) = -4
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[(x-2)*6-(6x)(1)]/(x-2)^2 = -4
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[6x-12-6x] = -4(x-2)^2
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-12 = -4(x-2)^2
(x-2)^2 = 3
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x-2 = sqrt(3) or x-2 = -sqrt(3)
x = 2+sqrt(3) or x = 2-sqrt(3)
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Solution in (3,5) is x= 2+sqrt(3)
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Cheers,
Stan H.