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October 12th, 2017, 05:12 PM   #1
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Completely Stuck Derivatives

My professor gives us sets of questions to answer and I'm stuck on three of them. Normally I'd just google what to do but I couldn't find anything. Here are the questions with everything given. If someone could just point me in the right direction I'd really appreciate it.

Last edited by redArch; October 12th, 2017 at 05:15 PM.
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October 12th, 2017, 05:29 PM   #2
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Math Focus: Dynamical systems, analytic function theory, numerics
1. Take 2 derivatives and evaluate.

2. Compute $\frac{f(x+h) - f(x)}{h}$ using the formula given and apply the property given to take this limit as $h \to 0$.

3. Suppose I told you that this expression was equal to
\[ \lim_{h \to 0} \frac{f(a+h) - f(a)}{h} \]
for some unknown function and unknown value of $a$. Can you find an $f$ and an $a$ which make this true? This answer won't be unique and in fact there are infinitely many functions which work. But all of them have the same derivative and hence the same limit.
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October 13th, 2017, 07:52 PM   #3
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Thanks for the help, I got some of the questions with your help.
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