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HS Calculus

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Definition of the derivative to calculate f'(x) if f(x) = square root 2x. Find the equation of the tangent & normal line to the graph of f at x=2.

Tangent line - y=2x-x
Normal line - y = 1/2x +3

I do not know whether these are the correct answers.

  • HS Calculus -

    no.

    y = √(2x) = (2x)^(1/2)
    y' = (1/2)(2x)^(-1/2)(2) = 1/√(2x)
    when x=2, y = 2, y' = 1/2

    so the tangent line is
    y = (1/2)x + b
    which at (2,2) is 2 = (1/2)(2) + b
    b = 1

    so the tangent equation is y = (1/2)x + 1

    the normal would have slope of -2
    so at (2,2)
    2 = -2(2) + b
    b = 6
    the normal has equation y = -2x + 6

  • HS Calculus -

    Thank you . I think that I understand alittle better. It is oblivious that I do not understand this material.

  • HS Calculus -

    I have one more that I really am lost at.
    Question - find the points on the graph y=2x^3-3x^2-12x+20 at which the tangent is parallel to tthe x-axis. I do not even know where to begin. We were told we could use the shortcut for this one.!

    Thanks again

  • HS Calculus -

    If a tangent is parallel to the x-axis, wouldn't it have a slope of zero?

    And isn't the slope represented by the first derivative?

    so differentiate, set that equal to zero and solve for x

    find the y's for those x's and simply say

    y = (whatever the y values are)

    let me know if you don't get y = 0 and y = 27

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