Calculus

Application of Derivatives

Easy

A student Sumit is running on a playground along the curve given by $y = x^2 + 7$ . Another student Amit standing at a point with co-ordinates $(3, 7)$ on the playground wants to hit Sumit by paper ball, when Sumit is nearest to him.

Based on the above information answer the following.

If D is the distance between Sumit and Amit, then the value of $x$ for which D is minimum, is :

$3$

$5$

$1$

$2$

✅ Correct Option: 3

Minimize $D^2 = (x-3)^2 + x^4$ . $\frac{d(D^2)}{dx} = 2(x-3) + 4x^3 = 0 \Rightarrow 4x^3 + 2x - 6 = 0 \Rightarrow 2x^3 + x - 3 = 0$ . $x = 1$ is a root: $2+1-3 = 0$ . Hence $x = 1$ .

Question 46

Sumit's position, when $x = 10$ is :

Question 47

Distance between Sumit and Amit in terms of $x$ is :

Question 49

The position of Sumit when Amit will hit the paper ball is :

Question 50

Minimum value of D is :

If D is the distance between Sumit and Amit, then the value of xxx for which D is minimum, is :

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If D is the distance between Sumit and Amit, then the value of $x$ for which D is minimum, is :