Determine the equation of the tangent to a curve at a point.

Question

I have the following problem.

Determine the equation of the tangent to the curve defined by $f(x)=x^2-6x+14$ at the point $(1,9)$, and then sketch it.

I'm having trouble with this question as I have no lessons whatsoever on it, the only example is telling me to complete the square to sketch it, and its not working out when I try that. Any help would be appreciated.

Is this question from a calculus based course or a regular algebra course? — imranfat, Mar 21 '17 at 21:28

score 1 · Answer 1 · answered Mar 21 '17 at 21:23

1

Take the derivative of $f(x): f'(x)=2x-6.$ So we have that the slope is $m=f'(1)=-4.$ Now, the equation of the tangent is $y=9+(-4)(x-1)=-4x+13.$

answered Mar 21 '17 at 21:23

Riccardo Ceccon

1,538

1

If you prefer to avoid derivatives, feel free to ask! – Riccardo Ceccon Mar 21 '17 at 21:24

Determine the equation of the tangent to a curve at a point.

1 Answers1