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DERIVATIVES
If f'(x) > 0 or f'(x) < 0 for all x, then the inverse function exists.
How derivatives can help you determine if a function is invertible?
Derivatives are a great tool to prove functions have an inverse. If the derivative of a function is monatomic (meaning it is only positive or negative) and the function is differentiable, we can prove that the function has an inverse.
The Chain Rule
Real-World Applications
The Stock Market.
A wall street analyst has determined that the hot new tech company's stock is following the curve of ln(x^10)-x and is expected to drop rapidly due to the coronavirus. You own a significant number of shares and want to sell before you lose it all. He predicts that the company will drop in 21 weeks. When would be the optimum time to sell out?
ANSWER
This example is compelling due to the importance of the stock market in everyone's life. The better we can predict trends the more money we will be able to make.
Problem Correction
Incorrect
the derivative of 4^ex is incorrect
Correction
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