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The slope of the tangent to the curve `y=-x^(3)+3x^(2)+9x-27` is maximum when `x` equals |
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Answer» Correct Answer - 1 If `m` be the slope of the tangent to the given curve, then `m=(dy)/(dx)=-3x^(2)+6x+9` `implies(dm)/(dx)=-6x+6,(d^(2)m)/(dx^(2))=-6` Now, `(dm)/(dx)=0implies-6x+6=0impliesx=1` Also then `(d^(2)m)/(dx^(2))lt0`, so at `x=1` the slope `m` will be maximum. |
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