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 $y=12x+4$ .

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