How do we determine the function, minimum or maximum, and the value of the minimum or maximum?

Question 1

How do we determine the function, minimum or maximum, and the value of the minimum-example-1

Question 2

$\begin{gathered} f(x)=2x^2-12x+19 \\ a) \\ The\text{ given function has the form} \\ f(x)=ax^2+bx+c \\ when\text{ a>0, the function opens upward. In this case a=2,} \\ \text{hence, the function has a minimum} \\ b) \\ The\text{ minimum of this fuction will be its vertex} \\ V=((-b)/(2a),f((-b)/(2a))) \\ a=2 \\ b=-12 \\ (-b)/(2a)=(-(-12))/(2(2))=(12)/(4)=3 \\ f((-b)/(2a))=f(3)=2(3)^2-12(3)+19=2(9)-36+19=18-36+19 \\ f(3)=1 \\ Hence \\ The\text{ function^^b4s minimum value is 1} \\ \\ c) \\ The\text{ minimun value occurs at x=3} \end{gathered}$

How do we determine the function, minimum or maximum, and the value of the minimum-example-2

How do we determine the function, minimum or maximum, and the value of the minimum or maximum?

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