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If f(6) = 3, What is the equation of the tangent line to the graph y=f(x) at x=6? I...

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undeadable | (Level 1) Honors

Posted July 10, 2013 at 12:16 AM via web

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If f(6) = 3, What is the equation of the tangent line to the graph y=f(x) at x=6? I forgot how to find the slope.

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mjripalda | High School Teacher | (Level 1) Senior Educator

Posted July 10, 2013 at 1:48 AM (Answer #1)

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The notation f(6)=3 indicates that the point of tangency on the curve y=f(x) is (6,3) .

And the slope of the line at the point of tangency is is m=y'.

So, take the derivative of y.

`y=f(x)`

`y'=f'(x)`

Then, plug-in x=6.

`y'=f'(6)`

Since the expression for f(x) is not given, there is no specific value for y'.

Hence, the slope of the tangent line is f'(6).

Now that the slope and point of tangency are known, apply the point-slope form to get the equation of the tangent line.

`y-y_1=m(x-x_1)`

`y-3=f'(6)(x-6)`

`y-3=xf'(6)-6f'(6)`

`y=xf'(6)-6f'(6)+3`

Therefore, the equation of the tangent line is `y=xf'(6)-6f'(6)+3` .

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