Wednesday, October 8, 2008

Slippery Slopes

For this assignment, we had to find the derivative for the equation y = 2^x, an exponential function. Most students used the "find the slope of a secant for two very close points" method. Other students use the calculator to get the derivatives. Can you do both methods?

We then tried to examine the relationship between the y-value and the derivative. Some noticed some interesting patterns -- the y-values double and the derivatives double. What makes the y-values double? For #2, the equation is y = 10^x. What patterns for the y-values did you see or would you expect to see? What patterns for the derivatives did you see or would you expect to see?

Finally, our goal was to create an equation. For 1b, some said that the equation is:
Derivative = (y / 1.44)

Some others said:
Derivative = 0.693 * y

Which is correct?

Can you create the equation for the derivative in terms of the y-value for problem #2?

Can you generalize the derivative of any exponential function (y = A^x)?

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