Question

After graphing the functions, how would I determine the zeroes and min/max's of the following equations. I only need to know how.

f(x) = sinx + ln(x/2) f(x) = cos(2x) - sqrt3 + ln|x|

Answer 1

Zeroes are where f(x)=0, and extreme points are where first derivative of f(x)=0. Minimums are where second derivative >0, minimums where second derivative <0, and inflection points where second derivative =0.

Answer 2

I'm aware of that, but there are innumerable amounts within each equation, this is not basic algebra.

Answer 3

Ok, had to make sure you knew the general procedure.
If there are multiple zeroes and they occur periodically, then you'll need to express the solutions as a period function or some sort of recursive formula.

Answer 4

Not even, the Absolute Maximum And Minimums are necessary, as well as the zeroes. All in radians.

Answer 5

Do you want to use Calculus for this? I know I method.

Answer 6

Calculus is what I'd need to do, this is pre-calculus material supposedly.

Answer 7

I know the method*

Answer 8

Please share.

Answer 9

OK, I'm too sleepy to teach... but here is where I learnt it from: http://tutorial.math.lamar.edu/Classes/CalcI/MinMaxValues.aspx

Answer 10

Oh, you only need the absolute extrema, not all the relative extrema?

Answer 11

The Absolute Extrema would most likely be all I need.

Answer 12

Ok, that's a lot easier then.
Let's look at the first one. Your domain is restricted by the LN function. X>0.

Answer 13

As it approaches 0 from the right it plunges into negative infinity asymptotically. So it doesn't really have an absolute minimum. Likewise, it seems to grow slowly, but without bound, so there's no absolute maximum either.

Answer 14

How can I be certain? Can you make a graph that would further explain that?

Answer 15

I'll try.