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Math Help - differentiable functions

  1. #1
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    differentiable functions

    The twice-differentiable function f is defined for all real numbers and satisies the following conditions:

    f(0) = 2
    f'(0) = -4
    f''(0) = 3

    The function h is given by h(x) = cos(kx)f(x) for all real numbers. where k is a constant. Find h'(x).
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  2. #2
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    Use the product rule on h(x)
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  3. #3
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    is the derivative:

    cos(kx) * f'(x) - kf(x) * sin(kx)
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  4. #4
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    yes
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  5. #5
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    how can i find the equation for the line tangent to the graph of h at x = 0 ?
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  6. #6
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    use y - y1 = m(x-x1)
    x1 = 0, chuck x1=0 into your h equation to get y1.
    then chuck x1 = 0 into your h' equation to get m.
    sub everything in and rearrange.
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  7. #7
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    do you get y = 2
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  8. #8
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    no
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  9. #9
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    for y1, i get 2

    and for m, i get 0

    what am i doing wrong?
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  10. #10
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    your m is wrong.
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  11. #11
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    h'(x) = cos(kx) * f'(x) - kf(x) * sin(kx)

    cos(k*0) * f'(0) - kf(0) * sin(k*0)

    cos(0) * f'(0) - kf(0) * sin(0)

    1 * -4 - 2k * 0

    -4 = m

    y - 2 = -4(x-0)

    y-2 = -4x

    y=-4x+2

    correct? and by the way thanks for everything
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  12. #12
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    correct, good job.

    Note: if your gradient is 0. you'll have a horizontal tangent & if your gradient is undefined/infinity then you'll have a vertical tangent. vertical tangents are of the form x = x1
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