Question

The graph of f (x) = 2x is shown below. Which of the following are true?
I. f (0) > 0
II. f '(0) > 0
III. f "(0) > 0

Answer 1

One of these choices is clearly true (i.e. f(0)>0 since \(\large 2^0=1>0\)). To check the others, you need to find the first and second derivatives of \(\large 2^x\). Do you remember the formula for this? :-)

Answer 2

first derivative: 2^x log(2)

Answer 3

Right, and second derivative is \(\large 2^x(\log 2)^2\). So is \(f^{\prime}(0)>0\) and \(f^{\prime\prime}(0)>0\)?

Answer 4

yes

Answer 5

Indeed, so it turns out that all three options are true. :-)

Answer 6

:)

Answer 7

Math is really tiring.

Answer 8

I hear ya...but after doing it for 7 years like I have, you get used to it...eventually. XD

Answer 9

What math are you in?

Answer 10

I have a masters degree in math; I'm not in school anymore (for the time being; I think I may go back for a Ph.D. sometime in the future, but we'll see how things go). XD

I'm currently looking for a tenure track position at a community college.

Answer 11

Wow! That is so cool! I am just in high school

Answer 12

Those were the days...I'd like to forget. :-P

Answer 13

I am really tired too and I am having a hard time concentrating on my math. Haha! I have been good at math the past few years but I had a really bad first few months in calculus and I didn't learn anything until december.