A function f(x)= x(1+ x), x [0,] has a local maxima at x= Option 1: 0 Option 2: /3 Option 3: -/3 Option 4:

Answer: /3. Solution: f'(x)= x+2x=(2 x-1)( x+1). On [0,] this vanishes at x=3 and x=. Around x=3 the sign changes from positive to negative, so it is a local maximum.

Calculus

Application of Derivatives

Medium

core

A function $f(x)=\sin x(1+\cos x), x \in [0,\pi]$ has a local maxima at $x=$

$\pi/3$

$-\pi/3$

$\pi$

✅ Correct Option: 2

$f'(x)=\cos x+\cos2x=(2\cos x-1)(\cos x+1)$ . On $[0,\pi]$ this vanishes at $x=\frac\pi3$ and $x=\pi$ . Around $x=\frac\pi3$ the sign changes from positive to negative, so it is a local maximum.

2026: 18 May Shift 1

A solid sphere of gold of radius 5 cm, is being melted in a furnace such that the radius is decreasing uniformly. When the radius is 1cm, the rate at which surface area (A) is decreasing w.r.t. time ( $t$ ) is equal to

( $\frac{dv}{dt}$ = rate at which volume is decreasing w.r.t. $t$ )

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The minimum value of $x^2 - 8x + 17$ on the set $\mathbb{R}$ of all real numbers is:

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If the function $f(x)$ defined by $f(x) = x^3 - 3x + 100, (x \in \mathbb{R})$ , (Where $\mathbb{R}$ is set of real numbers), then $f(x)$ has

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For the function $f(x)=x^3-2x^2-4x-5$ , which of the following statement is not correct ?

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The function $f(x) = x^4 - 2x^2$ is increasing on

2023: 22 May Shift 3

Interval in which the function $f(x) = 2x^3 - 3x^2 - 12x + 10$ is decreasing is :

A function f(x)=sin⁡x(1+cos⁡x),x∈[0,π]f(x)=\sin x(1+\cos x), x \in [0,\pi]f(x)=sinx(1+cosx),x∈[0,π] has a local maxima at x=x=x=

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CUET Mathematics Past Year Questions (Topic-Wise)

A function $f(x)=\sin x(1+\cos x), x \in [0,\pi]$ has a local maxima at $x=$