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.

Minimum value of D is :

$5$

$\sqrt{5}$

$3$

$1$

✅ Correct Option: 2

At $x = 1$ : $D = \sqrt{(1-3)^2 + 1^4} = \sqrt{4 + 1} = \sqrt{5}$ .

Question 46

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

Question 47

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

Question 48

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

Question 49

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

Minimum value of D is :

Solution

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