For the curve $y=5 x-2 x^3$, if $x$ increases at the rate of 2 units/sec, the rate of change in the slope of the curve at $x=3$ is ......../sec

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Aicharya · Accepted Answer

$y=5 x-2 x^3$ $\frac{d y}{d x}=5-6 x^2$ $	herefore$ Slope of curve is $5-6 x^2$. $	herefore \quad m=5-6 x^2 \Rightarrow \frac{d m}{d t}=(-12 x) \frac{d x}{d t}$ $\left(\frac{d m}{d t}ight)_{x=3}=-12(3) 	imes 2=-72$ $\left[\because \frac{d x}{d t}=2ight]$ $\Rightarrow$ Rate of change of slope at $x=3$ is -72

For the curve $y=5 x-2 x^3$, if $x$ increases at the rate of 2 units/sec, the rate of change in the slope of…

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