Problem 4
Give an example of a function \(f(x)\) where \(f^{\prime}(x)=0\).
Problem 4
T/F: Implicit differentiation can be used to find the derivative of \(y=x^{3 / 4}\).
Problem 4
If (1,10) lies on the graph of \(y=f(x)\) and \(f^{\prime}(1)=5,\) what can be said about \(y=f^{-1}(x)\) ?
Problem 4
Given \(f(5)=10\) and \(f^{\prime}(5)=2,\) approximate \(f(6)\).
Problem 4
What derivative rule is used to extend the Power Rule to include negative integer exponents?
Problem 5
T/F: Regardless of the function, there is always exactly one right way of computing its derivative.
Problem 5
Let \(y=f(x)\). Give three different notations equivalent to \(" f^{\prime}(x)\).
Problem 5
\(\mathrm{T} / \mathrm{F}: \frac{d x}{d y}=\frac{d x}{d t} \cdot \frac{d t}{d y}\)
Problem 5
Verify that the given functions are inverses. $$f(x)=2 x+6 \text { and } g(x)=\frac{1}{2} x-3$$
Problem 5
Given \(P(100)=-67\) and \(P^{\prime}(100)=5\), approximate \(P(110)\).
