# A Find the minimum without Calculus or Graphing

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1. Nov 16, 2015

### patrickbotros

• Poster is on a 10-day vacation from the PF for repeatedly misplacing schoolwork type questions
ƒ(ß)=.5sec(ß) + √[1+(sec2(ß)/4)+tan(ß)/√(2)]
Without graphing it or using calculus find the minimum. I already know the answer but want to know how to do it. It s at π/12 and is something like 1.5.
First off this is NOT a homework problem. I already know the answer is something like 1.5 at π/12 but I want to know how to do it. DONT PUT THIS IN A HOMEWORK SECTION.

2. Nov 17, 2015

### Dr. Courtney

Perhaps one can use trig identities to simplify it first.

3. Nov 17, 2015

### BvU

I'd like to know the actual function. Probably not
or, as we write it here $${1\over 2\cos\beta}+ \sqrt{ 1 + {1\over 4 \cos^2\beta} + {1\over \sqrt 2}\tan\beta}$$ surely ?

4. Nov 17, 2015

### nasu

Probably not.
f(Pi/12)=1.73
f(0)=1.62

@OP
Have you checked if the Pi/12 and 1.5 satisfy the expression?

5. Nov 17, 2015

### Dr. Courtney

Make a large table of values at small step size.

Pick the three lowest adjacent values.