\[\begin{array}{1 1}(1)-90units/sec&(2)90 units/sec\\(3)180units/sec&(4)-180units/sec\end{array}\]

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$y= 6x-x^3$

$\large\frac{dy}{dt} $$=6. \large\frac{dx}{dt}$$ -3x^2 \large\frac{dx}{dt}$

$\large\frac{dy}{dx} $$=(6-3x^2) \large\frac{dx}{dt}$

Slope $m= \large\frac{dy}{dx}=\frac{dy/dt}{dx/dt}$$= 6-3x^2$

$m= \large\frac{dy}{dx} $$=6-3x^2$

$ \large\frac{dm}{dt} $$=-6x. \large\frac{dx}{dt}$

Given $\large\frac{dx}{dt} $$=5 ,x=3$

$\large\frac{dm}{dt} $$=-6(3) .5m =-90 \;units /sec$

Hence 1 is the correct answer.

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