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Q.
For the curve $y=5 x-2 x^3$, if $x$ increases at the rate of $2$ units/s, then the rate at which the slope of curve is changing when $x=3$, is
Application of Derivatives
Solution:
Slope of curve $=\frac{d y}{d x}=5-6 x^2$
$ \Rightarrow \frac{d}{d t}\left(\frac{d y}{d x}\right)=-12 x \cdot \frac{d x}{d t} $
$ =-12 \text {. (3) . (2) }=-72 \text { units } / s $
Thus, slope of curve is decreasing at the rate of 72 units/s when $x$ is increasing at the rate of 2 units/s.