Posted by Ifi on Sunday, October 28, 2012 at 10:55am.
If f(x)=3x^25x, find the f'(2) & use it to find an equation of tangent line to the parabola
y=3x^25x at the point (2,2).
My ans is f'(2)=7 & y=7x12.
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....

Math  Steve, Sunday, October 28, 2012 at 12:07pm
excuse me? You're in calculus, and don't know what a parabola is?
Regardless, just work with the math.
y'(x) = 6x5
y'(2) = 7
y(2) = 2
So, you want the equation of the line passing through (2,2) with slope 7:
(y2) = 7(x2)
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.