# The shape of the functions

1. How many of the following functions on R are increasing on their domain? $y = e^x$, $y = x^2$, $y = x^3$ (a) 0 (b) 1 (c) 3 (d) 2
2. How many of the following functions on R are concave up on their domain? $y = e^x$, $y = x^2$, $y = x^3$ (a) 3 (b) 1 (c) 0 (d) 2

So I have these two questions above from a past exam, the solution for both of them is D, but I was very certain that only $e^x$ fullfilled the first question, this is because $x^3$ and $x^2$ also decrease in their domain as well as they increase; for example at the point (-1,1) of $x^2$ the function is decreasing; for $x^3$ at the point (0,0) the function is flat, and even $e^x$ remains flat at some point on its domain before starting growing up exponentially...regarding question 28 I think that only 1, this is $x^2$ has a concave up shape in their domain....I am a bit confused here, can anyone shine some light on it?

Thanks :)

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