Question

The Maximum slope of y = – x³ + 8x² – 13x – 18 is –

• A. 24
• B. – 24
• C. $\frac{25}{3}$
• D. None of these`

Answer 1

Answer: (C)

$\frac{25}{3}$

Answer 2

y = –x³ + 8x² – 13x – 18

m = $\frac{dy}{dx}$ = – 3x² + 16 x – 13

$\frac{dm}{dx}$ = –6x + 16 = 0 ̃ x = 8/3 ̃ $\frac{d^{2}m}{dx^{2}}$ = – 6

(m) x = 8/3 = –3 × $\frac{64}{9}$ + 16 × $\frac{8}{3}$ – $\frac{13}{1}$ = $\frac{25}{3}$