Calculus problem

Calculus Level 2

A particle is moving along the curve:- y = x 2 y = x^{2} Find out the x coordinate of the point on this curve where y coordinate is changing two times as fast as x coordinate ,Assume that particle always move with uniform speed


The answer is 1.

Aman Sharma by Aman Sharma , 25, India

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2 solutions

Samarth Sangam
Aug 25, 2014

c o n s i d e r y = x 2 d i f f e r e n t i a t i n g w r t x w e g e t d y d x = 2 x c a l l t h i s a s e q u a t i o n 1 g i v e n y c o o r d i n a t e i s c h a n g i n g t w i c e a s x c o o r d i n a t e y = 2 x d i f f e r e n t i a t i n g w r t x w e g e t d y d x = 2 s u b s t i t u t e d y / d x i n e q u a t i o n 1 w e g e t x = 1 consider\quad y={ x }^{ 2 }\\ differentiating\quad wrt\quad x\quad we\quad get\\ \frac { dy }{ dx } =2x\quad call\quad this\quad as\quad equation\quad 1\\ given\quad y\quad coordinate\quad is\quad changing\quad twice\quad as\quad x\quad coordinate\\ y=2x\\ differentiating\quad wrt\quad x\quad we\quad get\\ \frac { dy }{ dx } =2\\ substitute\quad dy/dx\quad in\quad equation\quad 1\\ we\quad get\quad x=1

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David Patty
Dec 16, 2014

If y = x^2, then y' = 2x; and if y is changing twice as fast as x, then the ratio of the change in y to the change in x is 2. Hence 2x = 2, and x = 1.

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