91Ó°ÊÓ

Find an equation of the line tangent to the graph of \(f(x)=e^{2 x}\) at the point (0,1)

A company's total cost, in millions of dollars, is given by \(C(t)=200-40 e^{-t}\) where \(t\) is the time in years since the start-up date. (GRAPH CAN'T COPY). Find each of the following. a) The marginal \(\operatorname{cost} C^{\prime}(t)\) b) \(C^{\prime}(0)\) c) \(C^{\prime}(5) \quad\) (Round to the nearest thousand.) d) Find \(\lim _{t \rightarrow \infty} C(t)\) and \(\lim _{t \rightarrow \infty} C^{\prime}(t) .\) Why do you think the company's costs tend to level off as time passes?

Solve \(P=P_{0} e^{k t}\) for \(t\)

Differentiate. $$f(x)=e^{x / 2} \cdot \sqrt{x-1}$$

For each of the functions in Exercises \(109-112,\) graph \(f, f^{\prime}\) and \(f^{\prime \prime}\). $$f(x)=e^{x}$$