Question 1

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

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

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