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What is the tangent point on g(x)=(36/x-1) has an instantaneous rate of change of -9?

That is 36 on the numerator and x-1 on the denomonator 

 Nov 24, 2018
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We can write the function as

 

f(x)   =  36 ( x - 1)^(-1)

 

The derivative is    -36 ( x - 1)^(-2).....set this = - 9

 

-36(x - 1)^(-2)   = -9

36 (x - 1)^(-2) = 9        rearrange as

 

36/9  =  ( x - 1)^2

4 = ( x - 1)^2

The x's that solve this   are   x =  3  and x = -2 

 

When x = 3....y = 36 / [ 3 - 1]   =   18

When x = -2....y =  36 / [ -2 - 1]  =  -12

 

So....the two points of tangency are   ( 3, 18)   and (-2, -12)

 

Here is the graph : https://www.desmos.com/calculator/pzmmsxfr2z

 

 

cool cool cool

 Nov 24, 2018
edited by CPhill  Nov 24, 2018

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