Question

The tangents to the curve $y=x^3-6x^2+9x+4,0\le x\le 5$ has maximum slope at $x$ which is equal to

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is D $5$

$y=x^3-6x^2+9x+4$
$\begin{array}{}\frac{dy}{dx}=3x^2-12x+9& \text{(1)}\end{array}$
$\begin{array}{}\frac{d^{2}y}{d{x}^2}=6x-12& \text{(2)}\end{array}$
Put the values $2,3,4,5\text{in}\frac{dy}{dx}$
Therefore slope is maximum at $x=5.$