Find the value of x and y for function, y = x3 + 21 where, the rate o

1.	Find the value of x and y for function, y = x3 + 21 where, the rate of change ofy is three times as the rate of change of x.
Answer» Given, function y = x³ + 21 Diff w.r.t. t, dy/dx = 3x² (dx/dt)…..(i) According to question dx/dt = 3(dx/dt) …..(ii) From equation (i) and (ii) 3x² = 3 ⇒ x = ± 1 In equation y = x³ + 21 Putting x = 1 y = 1³ + 21 = 1 + 21 =22 Putting x = -1 y = (- 1)³ + 21 = -1 + 21 = 20 So, x = ± 1 and y = 22, 20

Find the value of x and y for function, y = x3 + 21 where, the rate of change ofy is three times as the rate of change of x.

Answer»

Given, function y = x³ + 21

Diff w.r.t. t,
dy/dx = 3x² (dx/dt)…..(i)

According to question

dx/dt = 3(dx/dt) …..(ii)

From equation (i) and (ii)

3x² = 3

⇒ x = ± 1

In equation y = x³ + 21

Putting x = 1

y = 1³ + 21

= 1 + 21 =22

Putting x = -1

y = (- 1)³ + 21 = -1 + 21 = 20

So, x = ± 1 and y = 22, 20