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For the function g(x)=x^3-2x^2-1, at what tangent point is the instantaneous rate of change equal to -1?

 Nov 24, 2018
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The derivative of the function is

 

3x^2 - 4x....set this equal to  - 1   and solve for x

 

3x^2 - 4x  = -1    

 

3x^2 - 4x + 1    =    0

 

(3x - 1) ( x - 1)   = 0

 

Setting each factor to 0 and solving for x produces

 

 x = 1/3       or         x  = 1

 

And when x = 1/3, y = -32/27

 

And when x = 1, y = -2

 

So.....we have two points where this is true

 

(1/3, -32/27)    and ( 1, - 2 )

 

 

cool cool cool

 Nov 24, 2018

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