Think back to the days before calculators. The only operations that you can do on numbers are addition, subtraction, multiplication, division and exponentiation. So that means that any function you can evaluate must be from some combination of these operations.

The most general form of a combination of these numbers is a polynomial. So assume that the function can be written as a polynomial.

. Now you need to try to evaluate these constants.

You already know some information about the exponential function - that and that . You can use this information to evaluate the constants.

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Now differentiate both sides...

, and set again...

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Differentiate both sides...

. Let ...

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Differentiate both sides...

. Let ...

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Differentiate both sides...

. Let ...

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Are you starting to see a pattern?

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