What is the equation of the line tangent to #f(x)= 12x+4 # at #x=7#?

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Answer 1 · 2016-01-17T20:11:10

#y=12x+4#

#y=12x+4#.
This is clear from the fact that the function of #f# is linear, however, I will show the proof of it below.

The gradient of the tangent is represented by the derivative.

#f'(x)=12and f'(7)=12#.

So the gradient of the tangent to the curve is #12#.

But, #f(7)=12(7)+4=88#, so the point #(7,88)# lies on the curve and on the tangent.

We may hence substitute it into the general equation of the tangent, which is a straight line, of form #y=mx+c#.

#therefore 88=12(7)+c#

#therefore c=4#.

Hence the required tangent has equation #y=12x+4#.