For the curve y=5 x-2 x3, 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

Question

For the curve y=5 x-2 x3, 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 (A) -78 units/s (B) -72 units/s (C) -36 units/s (D) -18 units/s

Tardigrade Admin · Accepted Answer

Slope of curve =(d y/d x)=5-6 x2 ⇒ (d/d t)((d y/d x))=-12 x ⋅ (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.

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

$- 78$ units/s

$- 72$ units/s

$- 36$ units/s

$- 18$ units/s

Slope of curve $= \frac{d y}{d x} = 5 - 6 x^{2}$
$\Rightarrow \frac{d}{d t} (\frac{d y}{d x}) = - 12 x \cdot \frac{d x}{d t}$
$= - 12 . (3) . (2) = - 72 units / s$
Thus, slope of curve is decreasing at the rate of 72 units/s when $x$ is increasing at the rate of 2 units/s.

Q. For the curve y=5x−2x3, 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

−78 units/s

−72 units/s

−36 units/s

−18 units/s