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In Exercises 25 through 32, find the rate of change dy/dx where x = x_0 25. y = 3; x_0 = 2 26. y = -17; x_0 = 14 27. y = 3x + 5; x_0 = -1 28. y = 6 - 2x; x_0 = 3 29. y = x(1 - x); x_0 = -1 30. y = x^2 - 2x; x_0 = 1 31. y = x - 1/x; x_0 = 1 32. y = 1/(2-x); x_0 = -3 33. Let f(x) = x^2. a. Compute the slope of the secant line joining the points on the graph of f whose x coordinates are x = -2 and x = -1.9. b. Use calculus to compute the slope of the line that is tangent to the graph when x = -2, and compare with the slope found in part (a). 34. Let f(x) = 2x - x^2. a. Compute the slope of the secant line joining the points where x = 0 and x = 1/2. b. Use calculus to compute the slope of the tangent line to the graph of f(x) at x = 0, and compare with the slope found in part (a). 35. Let f(x) = x^3. a. Compute the slope of the secant line joining the points on the graph of f whose x coordinates are x = 1 and x = 1.1. b. Use calculus to compute the slope of the line that is tangent to the graph when x = 1, and compare with the slope found in part (a). 36. Let f(x) = x/(x-1). a. Compute the slope of the secant line joining the points where x = -1 and x = -1/2. b. Use calculus to compute the slope of the tangent line to the graph of f(x) at x = -1, and compare with the slope found in part (a). 37. Let f(x) = 3x^2 - x. a. Find the average rate of change of f(x) with respect to x as x changes from x = 0 to x = 1/16. b. Use calculus to find the instantaneous rate of change of f(x) at x = 0, and compare with the average rate found in part (a). 38. Let f(x) = x(1 - 2x). a. Find the average rate of change of f(x) with respect to x as x changes from x = 0 to x = 1/2. b. Use calculus to find the instantaneous rate of change of f(x) at x = 0, and compare with the average rate found in part (a). 39. Let s(t) = (t-1)/(t+1). a. Find the average rate of change of s(t) with respect to t as t changes from t = -1/2 to t = 0. b. Use calculus to find the instantaneous rate of change of s(t) at t = -1/2, and compare with the average rate found in part (a). 40. Let s(t) = sqrt(t). a. Find the average rate of change of s(t) with respect to t as t changes from t = 1 to t = 1/4. b. Use calculus to find the instantaneous rate of change of s(t) at t = 1, and compare with the average rate found in part (a).

          In Exercises 25 through 32, find the rate of change dy/dx where x = x_0
25. y = 3; x_0 = 2
26. y = -17; x_0 = 14
27. y = 3x + 5; x_0 = -1
28. y = 6 - 2x; x_0 = 3
29. y = x(1 - x); x_0 = -1
30. y = x^2 - 2x; x_0 = 1
31. y = x - 1/x; x_0 = 1
32. y = 1/(2-x); x_0 = -3
33. Let f(x) = x^2.
a. Compute the slope of the secant line joining the points on the graph of f whose x coordinates are x = -2 and x = -1.9.
b. Use calculus to compute the slope of the line that is tangent to the graph when x = -2, and compare with the slope found in part (a).
34. Let f(x) = 2x - x^2.
a. Compute the slope of the secant line joining the points where x = 0 and x = 1/2.
b. Use calculus to compute the slope of the tangent line to the graph of f(x) at x = 0, and compare with the slope found in part (a).
35. Let f(x) = x^3.
a. Compute the slope of the secant line joining the points on the graph of f whose x coordinates are x = 1 and x = 1.1.
b. Use calculus to compute the slope of the line that is tangent to the graph when x = 1, and compare with the slope found in part (a).
36. Let f(x) = x/(x-1).
a. Compute the slope of the secant line joining the points where x = -1 and x = -1/2.
b. Use calculus to compute the slope of the tangent line to the graph of f(x) at x = -1, and compare with the slope found in part (a).
37. Let f(x) = 3x^2 - x.
a. Find the average rate of change of f(x) with respect to x as x changes from x = 0 to x = 1/16.
b. Use calculus to find the instantaneous rate of change of f(x) at x = 0, and compare with the average rate found in part (a).
38. Let f(x) = x(1 - 2x).
a. Find the average rate of change of f(x) with respect to x as x changes from x = 0 to x = 1/2.
b. Use calculus to find the instantaneous rate of change of f(x) at x = 0, and compare with the average rate found in part (a).
39. Let s(t) = (t-1)/(t+1).
a. Find the average rate of change of s(t) with respect to t as t changes from t = -1/2 to t = 0.
b. Use calculus to find the instantaneous rate of change of s(t) at t = -1/2, and compare with the average rate found in part (a).
40. Let s(t) = sqrt(t).
a. Find the average rate of change of s(t) with respect to t as t changes from t = 1 to t = 1/4.
b. Use calculus to find the instantaneous rate of change of s(t) at t = 1, and compare with the average rate found in part (a).

In Exercises 25 through 32, find the rate of change dy/dx where x = x0
25. y = 3; x0 = 2
26. y = -17; x0 = 14
27. y = 3x + 5; x0 = -1
28. y = 6 - 2x; x0 = 3
29. y = x(1 - x); x0 = -1
30. y = x^2 - 2x; x0 = 1
31. y = x - 1/x; x0 = 1
32. y = 1/(2-x); x0 = -3
33. Let f(x) = x^2.
a. Compute the slope of the secant line joining the points on the graph of f whose x coordinates are x = -2 and x = -1.9.
b. Use calculus to compute the slope of the line that is tangent to the graph when x = -2, and compare with the slope found in part (a).
34. Let f(x) = 2x - x^2.
a. Compute the slope of the secant line joining the points where x = 0 and x = 1/2.
b. Use calculus to compute the slope of the tangent line to the graph of f(x) at x = 0, and compare with the slope found in part (a).
35. Let f(x) = x^3.
a. Compute the slope of the secant line joining the points on the graph of f whose x coordinates are x = 1 and x = 1.1.
b. Use calculus to compute the slope of the line that is tangent to the graph when x = 1, and compare with the slope found in part (a).
36. Let f(x) = x/(x-1).
a. Compute the slope of the secant line joining the points where x = -1 and x = -1/2.
b. Use calculus to compute the slope of the tangent line to the graph of f(x) at x = -1, and compare with the slope found in part (a).
37. Let f(x) = 3x^2 - x.
a. Find the average rate of change of f(x) with respect to x as x changes from x = 0 to x = 1/16.
b. Use calculus to find the instantaneous rate of change of f(x) at x = 0, and compare with the average rate found in part (a).
38. Let f(x) = x(1 - 2x).
a. Find the average rate of change of f(x) with respect to x as x changes from x = 0 to x = 1/2.
b. Use calculus to find the instantaneous rate of change of f(x) at x = 0, and compare with the average rate found in part (a).
39. Let s(t) = (t-1)/(t+1).
a. Find the average rate of change of s(t) with respect to t as t changes from t = -1/2 to t = 0.
b. Use calculus to find the instantaneous rate of change of s(t) at t = -1/2, and compare with the average rate found in part (a).
40. Let s(t) = sqrt(t).
a. Find the average rate of change of s(t) with respect to t as t changes from t = 1 to t = 1/4.
b. Use calculus to find the instantaneous rate of change of s(t) at t = 1, and compare with the average rate found in part (a).

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