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(a) Sketch, by hand, the graph of the function $ f(x) = e^x, $ paying particular attention to the graph crosses the y-axes.

What fact allows you to do this?

(b) What types of functions are $ f(x) = e^x $ and $ g(x) = x^e? $

Compare the differentiation formulas for $ f $ and $ g. $

(c) Which of the two functions in part (b) grows more rapidly when $ x $ is large?

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Missouri State University

Campbell University

Harvey Mudd College

Boston College

and slower. So when you read here so we're gonna draw a graph for part A. We have X is equal to eat the axe, and when Xs equal to zero, we have a wide value of one. The derivative is equal to eat the axe, so on access equal to zero, the derivative is equal to one, so it's increasing when it cuts the Y axis. For part B, we have f of X is exponential and it's defined for all ex Brian's and it's equal to FX. G of X is equal to X to the e and it's defined for only positive values of X, the derivative of F ISS needs the axe, then the derivative of G this e times x to the A minus one for part c Well, you see that FX is equal to eat. The X grows more rapidly when x this large compared to Jesus the X because when you see the graph up of X looks like this g of x, well, look like this