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It is given to you that 4x+10y= -26 is an equation of the tangent line to the graph of...

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masterpiece11 | Student | Salutatorian

Posted March 22, 2012 at 3:02 PM via web

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It is given to you that 4x+10y= -26 is an equation of the tangent line to the graph of y=g(x) at x=16.

It follows that y=__________

is the equation of the tangent line to y=(g(x))^2 at x=16

Tagged with calculus 1, math

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 22, 2012 at 11:53 PM (Answer #1)

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It is given that 4x + 10y= -26 is an equation of the tangent line to the graph of y=g(x) at x=16.

At x = 16, y = -9

=> g(16) = -9

4x + 10y = -26

=> y = -0.4x - 2.6

The slope of the line is -0.4

This implies that g'(16) = -0.4

For the curve defined by `y = (g(x))^2`

`dy/dx = 2*g(x)*g'(x)`

At x = 16, y = 81

`dy/dx = 2*(-9)*-0.4 = 7.2`

The equation of the tangent is `(y - 81)/(x - 16) = 7.2`

=> 10y - 810 = 72x - 1152

=> 72x - 10y - 342 = 0

=> 36x - 5y - 171 = 0

The required tangent is 36x - 5y - 171 = 0

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