The intervals for which f(x) = x^4 - 2x^2 is increasing are : Option 1: (-∞, 1) Option 2: (-1, ∞) Option 3: (-∞, -1) (0, 1) Option 4: (-1, 0) (1, ∞)

Answer: (-1, 0) (1, ∞). Solution: f'(x) = 4x^3 - 4x = 4x(x-1)(x+1). Sign chart: f'>0 on (-1, 0) (1, ∞) and f'<0 on (-∞, -1) (0, 1). Hence f is increasing on (-1, 0) (1, ∞).

Calculus

Application of Derivatives

Medium

core

The intervals for which $f(x) = x^4 - 2x^2$ is increasing are :

$(-\infty, 1)$

$(-1, \infty)$

$(-\infty, -1) \cup (0, 1)$

$(-1, 0) \cup (1, \infty)$

✅ Correct Option: 4

$f'(x) = 4x^3 - 4x = 4x(x-1)(x+1)$ . Sign chart: $f'>0$ on $(-1, 0) \cup (1, \infty)$ and $f'<0$ on $(-\infty, -1) \cup (0, 1)$ . Hence f is increasing on $(-1, 0) \cup (1, \infty)$ .

2026: 21 May Shift 2

Which of the following functions are strictly decreasing on $\left(0, \dfrac{\pi}{2}\right)$ ?

A. $\cos x$

B. $-\cot x$

C. $\cos 2x$

D. $\sin x$

Choose the correct answer from the options given below:

2026: 22 May Shift 2

At x = 1, the function $f(x)=x^4-48x^2+\alpha x+120$ attains its maximum value in the interval [0, 2], then the value of $\alpha$ is:

2025: 19 May Shift 1

Function $f(x) = x^3 - 3x + 3$ is

(A) Increasing in the interval $(-1, 1)$

(B) Increasing in the interval $(1, \infty)$

(D) Increasing in the interval $(-\infty, -1) \cup (1, \infty)$

Choose the correct answer from the options given below:

2026: 18 May Shift 1

If the function $f(x) = x^2-2kx+7$ is increasing on [1, 5] then $k$ belongs to

2026: 29 May Shift 1

The local maximum value of the function $f(x)=\dfrac{b^2}{a^4}(a^2x^2-x^4), a,b>0$ is equal to:

2025: 21 May Shift 2

The function $f(x) = x + \frac{1}{x}$ has

The intervals for which f(x)=x4−2x2f(x) = x^4 - 2x^2f(x)=x4−2x2 is increasing are :

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The intervals for which $f(x) = x^4 - 2x^2$ is increasing are :