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For the curve y=5x-2x^3 , if x increases...

For the curve `y=5x-2x^3` , if `x` increases at the rate of 2 units/sec, then how fast is the slope of the curve changing when `x=3?`

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Knowledge Check

  • A point P moves along the curve y=x^(3) . If its abscissa is increasing at the rate of 2 units/ sec, then the rate at which the slop of the tangent at P is increasing when P is at (1,1) , is

    A
    3 units/ sec
    B
    12 units/sec
    C
    24 units/sec
    D
    8 units/sec

  • What is the maximum slope of the curve y=-x^3+3x^2+2x-27 ?

    A
    1
    B
    2
    C
    5
    D
    -23

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