Maximum slope of the curve y = -x^3 + 3x^2 + 9x - 30 is Option 1: -6 Option 2: 0 Option 3: 12 Option 4: 16

Answer: 12. Solution: The slope is m=dy/dx=-3x^2+6x+9. Maximising m: dm/dx=-6x+6=0 gives x=1, and d^2m/dx^2=-6<0 confirms a maximum. Hence m_max=-3+6+9=12.

Calculus

Application of Derivatives

Medium

common

Maximum slope of the curve $y = -x^3 + 3x^2 + 9x - 30$ is

-6

✅ Correct Option: 3

The slope is $m=\frac{dy}{dx}=-3x^2+6x+9$ . Maximising $m$ : $\frac{dm}{dx}=-6x+6=0$ gives $x=1$ , and $\frac{d^2m}{dx^2}=-6<0$ confirms a maximum. Hence $m_{max}=-3+6+9=12$ .

2025: 29 May Shift 2

Match List-I with List-II

List-I	List-II
Function f(x)	Interval for increasing/decreasing of function f(x)
---	---
(A) $f(x) = x\vert x\vert$	(I) Decreases on $(0, \infty)$
(B) $f(x) = x^2 + 2x - 5$	(II) Increases on $(3, \infty)$
(C) $f(x) = x^2 - 6x + 9$	(III) Decreases on $(-\infty, -1)$
(D) $f(x) = -x^2$	(IV) Increases on $(-\infty, \infty)$

Choose the correct answer from the options given below:

2026: 12 May Shift 2

The total revenue received from the sale of $x$ units of a product is given by $R(x)=24x+5x^2+3$ . The marginal revenue when $x=10$ is,

2025: 22 May Shift 2

Match List-I with List-II

List-I	List-II
(A) Marginal average cost if cost function $C(x) = \frac{50}{\sqrt{x}}$	(I) $50\sqrt{x}$
(B) Marginal average cost if cost function $C(x) = 50\sqrt{x}$	(II) $-\frac{75}{x^2\sqrt{x}}$
(C) Revenue function if demand function $P=\frac{50}{\sqrt{x}}$	(III) $\frac{-25}{x\sqrt{x}}$
(D) Marginal revenue if demand function $P=50\sqrt{x}$	(IV) $75\sqrt{x}$

Choose the correct answer from the options given below:

2026: 30 May Shift 1

The function $f(x)=\cot^{-1}x+x$ increases in the interval:

2025: 13 May Shift 1

In which of the following intervals, the function $f(x) = -x^2 - 2x + 15$ is decreasing?

2025: 21 May Shift 2

The function $f(x) = 6 - 6x - 2x^2$

Maximum slope of the curve y=−x3+3x2+9x−30y = -x^3 + 3x^2 + 9x - 30y=−x3+3x2+9x−30 is

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

Maximum slope of the curve $y = -x^3 + 3x^2 + 9x - 30$ is