Question

Maximum slope of the curve $y = - x^{3} + 3x^{2} + 9x - 27$ is

• A. 0
• B. 12
• C. 16
• D. 32

Answer 1

Answer: (B)

12

Answer 2

$y = f(x) = - x^{3} + 3x^{2} + 9x - 27$

The slope of this curve $f^{'}(x) = - 3x^{2} + 6x + 9$

Let $g(x) = f^{'}(x) = - 3x^{2} + 6x + 9$

Differentiate with respect to x, $g^{'}(x) = - 6x + 6$

Put $g^{'}(x) = 0$ ⇒ $x = 1$

Now, $g^{''}(x) = - 6 < 0$ and hence at $x = 1,g(x)$

(Slope) will have maximum value.

$\therefore\lbrack g(1)\rbrack_{max.}$.