Determine the value of dy/dt at x=3 when y=2x^2-5x and dx/dt=2.

1 Answer

embizze's profile pic

embizze | High School Teacher | (Level 2) Educator Emeritus

Posted on

Determine `(dy)/(dt)` at x=3 if `y=2x^2-5x` and `(dx)/(dt)=2` .

Differentiate `y=2x^2-5x` with respect to `t` using implicit differentiation.

`(dy)/(dt)=4x(dx)/(dt)-5(dx)/(dt)` Here we can apply the general power rule: if `u` is a differentiable function of `t` then `d/(dt) u^n=n*u^(n-1)u'`

Substitute for the known values of x and `(dx)/(dt)` to get:



The derivative of y with respect to t of `y=2x^2-5x` at x=3 with `(dx)/(dt)=2` is 14.


This result can be interpreted as follows: let p be a point on the parabola given by `y=2x^2-5x` . The point is moving at 2 units per unit time with respect to the x-axis. We are asked to find the rate of change with respect to the y-axis when x=3. The result shows that the change in y is 14 units per unit time when x=3.