A particle moves along the curve y = x2 + 2x. At what point(s) on the curve are the x and y coordinates of the particle changing at the same rate?

Asked by Aaryan | 1 year ago |  76

##### Solution :-

Given a particle moves along the curve y = x2 + 2x.

To find the points at which the curve are the x and y coordinates of the particle changing at the same rate

Equation of curve is y = x2 + 2x

Differentiating the above equation with respect to x, we get

$$\dfrac{dy}{dx}=\dfrac{d(x^2+2x)}{dx}$$

When x and y co-ordinate of the particle are changing at the same rate

Substituting the value from equation (i)

2x + 2 = 1

2x = -1

x = $$-\dfrac{1}{2}$$

Substituting the value of x in the given of curve

Thus, the points at which the curve are the a and y co-ordinates of the particle changing at the same rate is ($$-\dfrac{1}{2}$$,$$-\dfrac{3}{4}$$).

Answered by Sakshi | 1 year ago

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