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.

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

$(5, 32)$

$(1, 8)$

$(3, 7)$

$(3, 16)$

✅ Correct Option: 2

From previous question, $x = 1$ minimizes distance. So $y = 1^2 + 7 = 8$ . Sumit's position is $(1, 8)$ .

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 50

Minimum value of D is :

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

Solution

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