The Maths Prof: Rates of Change, Derivatives (Part 2)

The Maths Prof2 minutes read

The x coordinates of point P on the curve y = 8/7 - 2x, with varying rates of change, are determined to be 1 and 6 through differentiation and solving the equation based on the rates provided.

Insights

  • The x coordinate of point P can be either 1 or 6 based on the rates of change provided in the equation.
  • The equation derived from the rates of change reveals that the x values of point P are crucial in determining the movement along the curve y = 8/7 - 2x.

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Recent questions

  • How does the point move along the curve?

    It moves with increasing x and y coordinates.

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Summary

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Point P's x coordinates: 1 and 6

  • The point moves along the curve y = 8/7 - 2x, with the x coordinate increasing at a rate of 0.125 units per second and the y coordinate increasing at a rate of 0.08 units per second.
  • Differentiating the curve equation to find Dy by DX as 16/(7 - 2x)^2, the equation is set up as 16/(7 - 2x)^2 = 0.08 / 0.125, leading to x values of 1 and 6.
  • By solving the equation derived from the rates of change, the possible x coordinates of point P are found to be 1 and 6.
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