Question 995804
Definition: Maximum and Minimum of a function

1. A function {{{f}}} has a maximum at {{{x=a}}} if {{{f(a)>=f(x)}}} for all {{{x}}} in the domain of {{{f}}}.

2. A function {{{f}}} has a minimum at {{{x=a}}} if {{{f(a)<=f(x)}}} for all {{{x}}} in the domain of {{{f}}}.

The values of the function for these x-values are called extreme values or extrema. 


{{{f(x) = 2x^2 -9x}}} here you have a parabola 

the least or greatest value of the parabola could be found at the vertex of the parabola (on the axis of symmetry {{{x=-b/2a}}})

{{{f(x) = 2x^2 -9x}}}=> {{{a=2}}} {{{b= -9}}}=>minimum is at {{{x=-b/2a}}}=>{{{x=-(-9)/(2*2)}}}=>{{{x=9/4}}}=>{{{x=2.25}}}

or, find it using derivative:

{{{f}}}'{{{(x) = 4x -9}}}

{{{0= 4x -9}}}=>{{{4x=9}}}=>{{{x=9/4}}}


{{{drawing( 600, 600, -10, 10, -15, 10,
line(2.25,10,2.25,-15),
 graph( 600, 600, -10, 10, -15, 10, 2x^2 -9x)) }}}