Question

find the maximum and minimums and identify as absolute or local. if there aren’t any, write none.

1. $f(x)=4 - x + x^{2}$
2. max:____

min:____

Explanation:

Step1: Find the derivative.

$f'(x)=-1 + 2x$

Step2: Set derivative equal to 0.

$-1+2x = 0$, so $x=\frac{1}{2}$

Step3: Find the second - derivative.

$f''(x)=2>0$, so it's a minimum.

Step4: Find the minimum value.

$f(\frac{1}{2})=4-\frac{1}{2}+\frac{1}{4}=\frac{15}{4}$

Answer:

Max: none
Min: $\frac{15}{4}$, absolute