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idku
 one year ago
just reviewing something from calc 1
(made up ex.)
idku
 one year ago
just reviewing something from calc 1 (made up ex.)

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idku
 one year ago
Best ResponseYou've already chosen the best response.0Should I make a function up? \(\tt f(x)=x^3+3x^2+2x+1\) now will do a lot of things to it...

idku
 one year ago
Best ResponseYou've already chosen the best response.0At first, I will just simply determine when the function is increasing and when decreasing, using the first derivative.

idku
 one year ago
Best ResponseYou've already chosen the best response.0\(\tt f'(x)=3x^2+6x+2\) This is the derivative, or the slope, of the function \(\tt f(x)\). We know from elementary maths before calculuses, that: \(\bullet\) When the slope is positive the function is increasing \(\bullet\) When the slope is negative the function is decreasing

idku
 one year ago
Best ResponseYou've already chosen the best response.0So, we will set \(\tt f'(x)>0\) to find where the function is increasing, and set \(\tt f'(x)<0\) to find where the function is decreasing.

idku
 one year ago
Best ResponseYou've already chosen the best response.0now, won't actually solve that... i need the concepts.

idku
 one year ago
Best ResponseYou've already chosen the best response.0Ok, now, the critical numbers.

idku
 one year ago
Best ResponseYou've already chosen the best response.0the critical numbers are the values of \(\tt f(x)\), are when: 1. \(\tt f'(x)=0\) (will have to set the derivative =0 and solve for x) 2. \(\tt f'(x)\) is undefined (provided that \(\tt f(x)\) has a value at that point) Polynomial is always continuous, and even without knowing this fact, I can tell that no restrictions in \(\tt f(x)\) or \(\tt f'(x)\) exist.

idku
 one year ago
Best ResponseYou've already chosen the best response.0Then \(\tt f'(b)=greatest~output~of~B\) \(\tt f'(a)=smallest~output~of~A\) when i check critical numbers, that would mean that I have absolute maximum of B at x=b absolute minimum of A at x=a
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