We came up with the equation for the derivatives of two functions:

f(x) = 3x + 4

g(x) = x^2 - 9

For the f(x) function, we found that the derivative is always 3, no matter what value of x we used.

Some classes developed a conjecture for all linear equations...For ALL linear equations, the derivative IS the slope.

For the g(x) function, we found that the equation for the derivative is 2x, and changes depending on the value of x.

One class developed this conjecture for all quadratic equations...For ALL quadratic equations, the derivative = 2*A*x, where A is the coefficient of the x^2 term.

NOTE: These are conjectures, which we will accept to be true until someone can find an example where it doesn't work. Can you find an example that will prove our conjecture to be false?

## Thursday, October 9, 2008

### HW20

Posted by MR. MARTI at 2:23 PM

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