Question

A point moves along the curve y=2x^2 in such a way that the y value is increasing at the rate of 8 units per second. At what rate is x changing when x = 1.5?

Answer 1

You know differentiation?

Answer 2

a little bit

Answer 3

We will differentiate both sides of your parabolic equation with respect to a parameter t (lets say time, because your question mentions rate of change)

Answer 4

Ok?

Answer 5

ok

Answer 6

So
on the left side is dy/dt....fine?

Answer 7

these are the answers to choose from by the way

Increasing 1.333… unit/sec
None of these.
Decreasing 3.5 unit/sec
Decreasing 1.333… unit/sec
Increasing 3.5 unit/sec

Answer 8

I dont need answers to choose from..and for all purposes, neither should you, ok?

Answer 9

on the left is dy/dt

on the right we use chain rule

dy/dt=4xdx/dt

Answer 10

ok

Answer 11

so now, u have values for dy/dt and x. U only dont know dx/dt. Isolate and find it

Answer 12

the derivative of x²=2x

im lost

Answer 13

Here is another solution:
We know dy/dt=8, dx/dt is what we need to find out.
Ok, We have y=2x^2-->dy/dx=4x
Based on chain rule, we have:
dy/dt=dy/dx multiply with dy/dt
==>8=4x * dx/dt-->dx/dt=8/4x (x=1.5)
-->dx/dt=1.33333

Answer 14

thanks very much to the both of you. both of your explanations combined made me understand