Find the maximum slope of the curve `y=-x^3+3x^2+2x-27.`

Options

A. 1
B. 2
C. 5
D. -23

Answer

C

Explanation

The equation of curve is given as :
`y=x^(3)+3x^(2)+2x-27`
on differentiating w.r.t.x we get
`(dy)/(dx)=-3x^(2)+6x+2`
This represents slope of the curve at any point
Let `A=(dy)/(dx)=3x^(2)+6x+2`
`rarr (dA)/(dx)=-6x+6`
and `(d^(2)A)/(dx^(2))=-6`
Put `(dA)/(dx)=0` for maxima or minima
`-6x+6=0`
`rarr` x=1
`therefore` A is maximum at x=1
`therefore` Maximum slope of curve =-3+6+2=5