The function f(x) = 6(2x^4 - x^2) is strictly increasing in Option 1: (-∞, -1/2) (1/2, ∞) Option 2: (-1/2, 0) (1/2, ∞) Option 3: (-1/2, 1/2) Option 4: (-∞, -1/2) (0, 1/2)

Answer: (-1/2, 0) (1/2, ∞). Solution: f'(x) = 6(8x^3 - 2x) = 12x(2x-1)(2x+1). Roots at x = -1/2, 0, 1/2. Sign analysis: f'(x) > 0 on (-1/2, 0) and (1/2, ∞).

Calculus

Application of Derivatives

Medium

The function $f(x) = 6(2x^4 - x^2)$ is strictly increasing in

$(-\infty, -\frac{1}{2}) \cup (\frac{1}{2}, \infty)$

$(-\frac{1}{2}, 0) \cup (\frac{1}{2}, \infty)$

$(-\frac{1}{2}, \frac{1}{2})$

$(-\infty, -\frac{1}{2}) \cup (0, \frac{1}{2})$

✅ Correct Option: 2

$f'(x) = 6(8x^3 - 2x) = 12x(2x-1)(2x+1)$ .

Roots at $x = -\frac{1}{2}, 0, \frac{1}{2}$ . Sign analysis: $f'(x) > 0$ on $(-\frac{1}{2}, 0)$ and $(\frac{1}{2}, \infty)$ .

2025: 26 May Shift 2

If it is given that at $x = 1$ , the function $f(x) = x^4 - 62x^2 + 2ax + b$ attains its maximum value on the interval [0, 2], then the value of a is:

2026: 19 May Shift 1

The height of a closed cylinder of given surface area and maximum volume is equal to the

2025: 13 May Shift 1

For the function $f(x) = sinx + cosx, x \in [0, \pi]$ , which one of the following is correct?

2025: 15 May Shift 1

The maximum value of $f(x) = \frac{1}{4x^2 + 2x + 1}$ is

2025: 19 May Shift 1

The semi vertical angle of a right circular cone of maximum volume of a given slant height is

2022: 25 May Shift 1

The equation of the tangent, to the curve $y = x^2 - 2x - 3$ which is perpendicular to the line $x + 2y + 3 = 0$ , is

The function f(x)=6(2x4−x2)f(x) = 6(2x^4 - x^2)f(x)=6(2x4−x2) is strictly increasing in

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

The function $f(x) = 6(2x^4 - x^2)$ is strictly increasing in