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Math Help - Questions in derivatives

  1. #1
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    Questions in derivatives



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  2. #2
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    Quote Originally Posted by r-soy View Post


    To #1a):

    The equation of the line is:

    y = -\frac1{24} x + 1

    Therefore the perpendicular direction to this line has the slope m = 24.

    Therefore you have to solve for x:

    f'(x)=24

    Remark: Probably you have solved f'(x)=0
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  3. #3
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    Quote Originally Posted by r-soy View Post

    To 1.b):

    The given line has the slope m = -12.

    Therefore you have to solve for x:

    f'(x) = -12

    To get the y-coordinaste of the points in question you plug in the x-coordinates into the term of f.
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  4. #4
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    my dear help me about Q 1 for a how we got m = 24 and for b = - 12

    plese write the step .
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  5. #5
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    for 1 a how we got m = 24 and for b = - 12 ?
    and what is the point for a and b ?


    2 ) are 2 and 3 the answre correct now:

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  6. #6
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    Quote Originally Posted by r-soy View Post
    my dear help me about Q 1 for a how we got m = 24 and for b = - 12

    plese write the step .
    Hopefully, the math gurus will help me, but I THINK that, since you're looking for the line that is perpendicular to y = 1 - (\frac{x}{24}), the slope of the line you're looking for will be the negative reciprocal of the slope of the line you have. So, for the equation of the line y = 1 - (\frac{x}{24}), you have that the slope is:

    -(\frac{x}{24}) = (-\frac{1}{24})x \Longrightarrow -\frac{1}{24}

    Now, the negative of this slope is -(-\frac{1}{24}) \Longrightarrow \frac{1}{24}

    The reciprocal, then, is 24.

    Again, let those who know correct me... ;-)
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  7. #7
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    For (1)(a) the problem asked where the tangent line was perpendicular to y= 1- x/24. You found x where the derivative was 0. I have no idea why you did that! The derivative is the slope of the tangent line. A line with slope 0 is horizontal and is perpendicular to a vertical line. y= 1- x/24 is NOT vertical. It has slope -1/24. Clearly you are expected to know that if y= mx+ b and y= nx+ d are perpendicular, then n= -1/m. A line perpendicular to a line with slope -1/24 must have slope 24. THAT was why everyone set the derivative equal to 24, not 0!

    For (1)(b), the problem asked where the tangent line was parallel to y= \sqrt{3}- 12x which has slope -12. Two lines are parallel if and only if they have the same slope.


    Again- two lines, y= mx+ b and y= nx+ c, are parallel if and only if m= n, perpendicular if and only if m= -1/n (equivalently mn= -1).
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  8. #8
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    thanls a lot plese .. see My participat Number 6
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  9. #9
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    is correct :

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