Question

If f(x)=3x^2-5x, find the f'(2) & use it to find an equation of tangent line to the parabola
y=3x^2-5x at the point (2,2).

My ans is f'(2)=7 & y=7x-12.
What is parabola exactly? & is the any possibility if the eqtn of f(x) is not the same with parabola eqtn? If yes, how to calculate the tangent equation ? Can u give any clue or tips or keywords for answering this kind of question....

Answer 1

excuse me? You're in calculus, and don't know what a parabola is?

Regardless, just work with the math.

y'(x) = 6x-5
y'(2) = 7

y(2) = 2

So, you want the equation of the line passing through (2,2) with slope 7:

(y-2) = 7(x-2)

Your answer is correct.

Any quadratic equation represents a parabola. Go to wolfram and type in some quadratic functions. You will see that they are all parabolas.