Calculus

Application of Derivatives

Easy

applied

Match List-I with List-II

List-I (Function) List-II (Critical point)
(A) $f(x)=x^3-3x$ (I) $x=3$
(B) $f(x)=x^3-12x$ (II) $x=0$
(C) $f(x)=x^2-6x$ (III) $x=1$
(D) $f(x)=x^2$ (IV) $x=2$

Choose the correct answer from the options given below:

(A) - (I), (B) - (III), (C) - (IV), (D) - (II)

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

(A) - (III), (B) - (IV), (C) - (II), (D) - (I)

(A) - (II), (B) - (I), (C) - (IV), (D) - (III)

✅ Correct Option: 2

Set $f'(x) = 0$ in each case.

(A) $3x^2-3 = 0 \Rightarrow x = \pm1$ , so $x=1$ is listed.

(B) $3x^2-12 = 0 \Rightarrow x = \pm2$ , so $x=2$ .

(D) $2x = 0 \Rightarrow x = 0$ .

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The point on the curve $\frac{x^2}{4} + \frac{y^2}{9} = 1$ at which the tangent to the curve is parallel to the x-axis is

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For the function $f(x) = 2x^3 - 9x^2 + 12x - 5$ , $x \in [0, 3]$ , match List-I with List-II :

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The function $f(x) = 4x + \frac{1}{x}$ is

(A). Increasing in the interval $\left(-\infty, -\frac{1}{2}\right)$

(B). Increasing in the interval $\left(-\frac{1}{2}, 0\right)$

(C). Decreasing in the interval $\left(0, \frac{1}{2}\right)$

(D). Decreasing in the interval $\left(\frac{1}{2}, \infty\right)$

Choose the correct answer from the options given below:

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The function $f(x) = tanx - x$

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The volume of a cube is increasing at the rate 9 $cm^3/s$ . How fast is the surface area increasing when the length of an edge is 10 cm ?

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If $2x + y = 6$ then the maximum value of $x^2 y$ is :

Solution