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

y=5 x-2 x^3 Given (d x)/(d t)=2 units / s slope of the curve =(d y)/(d x)=5-6 x^2=m (d m)/(d t)=-12 x (d x)/(d t)=-12 x(2)=-24 x at x=2, (d m)/(d t)=-24(2)=-48 Hence,slope of curveis decreasing at the rate of 48

CBSE 2025 · Region 4 · Set 1 · Q25 · 2 marks

For the curve $\displaystyle y=5 x-2 x^{3}$, if $\displaystyle x$ increases at the rate of $\displaystyle 2$ units $\displaystyle / \mathrm{s}$, then how fast is the slope of the curve changing when $\displaystyle x=2$ ?

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For the curve $\displaystyle y=5 x-2 x^{3}$, if $\displaystyle x$ increases at the rate of $\displaystyle 2$ units $\displaystyle / \mathrm{s}$, then how fast is the slope of the curve changing when $\displaystyle x=2$ ?

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