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

swimmers | Student | Honors

Posted March 21, 2012 at 1:40 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

A)     y=_______________ is the equation of the tangent line to y=g(x^2) at x=4

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

Tagged with calculus 1, math

cosinusix | College Teacher | (Level 3) Assistant Educator

Posted March 21, 2012 at 2:17 PM (Answer #1)

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at `x=16, ` the tangent curve intersect the graph of g therefore `y(16)=g(16).`

`10y+64=-26`

10y=-90

`y=-9`

The slope of the tangent line is `g'(16)=-4/10=-2/5`

g'(16)=-2/5

Let `f(x)=g(x^2).`

`f'(x)=2xg'(x^2)`

At `x=4, f'(4)=8g'(16)=-16/5`

`f(4)=g(16)=-9`

An equation of the tangent line of y=g(x^2) at x=4 is `y=-16/5 (x-4)-9`

Let `h(x)=g^2(x)`

`h'(x)=2g(x)g'(x)`

h'(16)=2*9*(-16/5)

`h'(16)=-288/5 `

`h(16)=g(16)^2=81`

`y=-288/5 (x-16)+81 ` is an equation of the tangent line to `y=g^2(x) ` at `x=16`