Based on the following given information answer the question Consider the function f(x) = x, x, x R. The slope of the tangent drawn at the point whose x coordinates is 2 on the curve y = x, x, . Option 1: 2 Option 2: -2 Option 3: 4 Option 4: -4

Answer: 4. Solution: For x > 0, y = x, x, = x^2. dy/dx = 2x. At x = 2, slope = 2 x 2 = 4.

Calculus

Application of Derivatives

Easy

Based on the following given information answer the question

Consider the function $f(x) = x|x|$ , $x \in R$ .

The slope of the tangent drawn at the point whose x coordinates is 2 on the curve $y = x|x|$ .

$-2$

$-4$

✅ Correct Option: 3

For $x > 0$ , $y = x|x| = x^2$ .

$\frac{dy}{dx} = 2x$ .

At $x = 2$ , slope $= 2 \times 2 = 4$ .

Question 46

The region bounded by curve $y = x|x|$ , x-axis and lines $x = \pm 1$ is best represented graphically by :

Question 47

The area of the region bounded by $f(x) = x|x|$ and x-axis from $x = 0$ to $x = 4$ is :

Question 48

The area of the region bounded by $f(x) = x|x|$ , x-axis and from $x = -1$ to $x = 1$ is :

Question 50

Consider the following statements for the curve $f(x) = x|x|$ and find that which of the following(s) are/is correct :

(A) $f(x) = x|x|$ is differentiable at $x = 0$ .

(B) $f(x) = x|x|$ is continuous at $x = 0$ but not differentiable at $x = 0$ .

(D) $f(x) = x|x|$ is symmetrical about y-axis.

Choose the correct answer from the options given below :