Use a CAS to perform the following steps in Exercises 59–60. a. Plot the equation with the implicit plotter of a CAS. Check to see that the given point P satisfies the equation. b. Using implicit differentiation, find a formula for the derivative dy/dx and evaluate it at the given point P. c. Use the slope found in part (b) to find an equation for the tangent line to the curve at P. Then plot the implicit curve and tangent line together on a single graph. 59. x3 - xy + y3 = 7, P (2, 1) 60. x5 + y3x + yx2 + y4 = 4, P (1,1)
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Use a CAS to perform the following steps in Exercises 59–60. a. Plot the equation with the implicit plotter of a CAS. Check to see that the given point P satisfies the equation. b. Using implicit differentiation, find a formula for the derivative dy/dx and evaluate it at the given point P. c. Use the slope found in part (b) to find an equation for the tangent line to the curve at P. Then plot the implicit curve and tangent line together on a single graph.
59. x3 - xy + y3 = 7, P (2, 1)
60. x5 + y3x + yx2 + y4 = 4, P (1,1)
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