The curve $C$ has equation $y={{x}^{3}}{{\mathrm{e}}^{-x}}$. Using differentiation, find the coo

Question

The curve $C$ has equation $y={{x}^{3}}{{\mathrm{e}}^{-x}}$. Using differentiation, find the coordinates of the stationary points on $C$ and determine their nature.[5] The region bounded by the curve $C$, the line $y=-x+2$ and the $x$-axis is rotated through $2\pi $ radians about the $x$-axis. Find the volume of the solid obtained.[3]

Accepted Answer

(a) $\left( 3,\,27{{	ext{e}}^{-3}} ight)$ is a maximum turning point. (ii) $0.651$ ($3$ s.f.)

2023 MI PRU2 P1 Q4

2023 MI PRU2 P1 Q4

Video Solution:

Solution:

Solution locked