Question

The maximum slope of the curve $-x^3+3x^2+2x-27$ is ${}^{\prime }{a}^{\prime }$ at $A(x,y)$ then

• A. $a=5,A(1,23)$
• B. $a=5,A(1,-23)$
• C. $a=5,A(-1,-27)$
• D. None of these

Answer 1

The correct option is B $a=5,A(1,-23)$

$y=-x^3+3x^2+2x-27$
$\frac{dy}{dx}=-3x^2+6x+2=-3(x^2-2x+1-1)+2=5-3(x-1{)}^2$
$\Rightarrow \frac{dy}{dx}\le 5$
Hence maximum value of slope of given curve is $a=5$ at $x=1$
and at $x=1$, $y=-23$, thus $A=(1,-23)$