Question

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

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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:
(dy)/(dt)=4(3)(2)-5(2)=24-10=14 
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The derivative of y with respect to t of y=2x^2-5x at x=3 with (dx)/(dt)=2 is 14.
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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.

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

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