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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....

  • Math -

    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.

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