Statement which is correctly identifies the local minimum of the graphed function is given by over the interval [tex][-1,0.5],[/tex] the local minimum is [tex]1[/tex].
" Graph is defined as the pictorial representation of the relation between the given variables on the coordinate plane along x-axis and y-axis."
According to the question,
Form the given graph of the function local minimum is given by
a. Over the interval [tex][-3, -2][/tex], the local minimum is [tex]0[/tex]:
From the graph value of y coordinate at [tex]x= -3[/tex] is closest to [tex]-6[/tex]. As per given statement local minimum is zero . [tex]-6 < 0[/tex]
At [tex]-2[/tex] closest to [tex]1[/tex] , [tex]1 > 0[/tex]
Therefore , local minimum [tex]=0[/tex] is not a correct option.
b. Over the interval[tex][-2, -1][/tex], the local minimum is [tex]2.2.[/tex]
From the graph at [tex]-2[/tex] closest to [tex]1[/tex] , [tex]1 \neq 2.2[/tex].
Moving from [tex]-2[/tex] to [tex]-1[/tex] graph is increasing . At [tex]-1[/tex] y - coordinate is equals to [tex]2[/tex].
Again [tex]2\neq 2.2[/tex]
Therefore, it is not a correct option.
c. Over the interval[tex][-1, 0.5][/tex], the local minimum is [tex]1[/tex]
From the graph at [tex]-1[/tex] closest to [tex]2[/tex] ,and keep on decreasing till [tex]x=0[/tex] .
From [tex]0[/tex] to [tex]0.5[/tex] graph keep on increasing.
At [tex]x= 0[/tex] value of y-coordinate is equals to [tex]1[/tex] , which represents the local minimum at [tex]x= 0[/tex] which is in the interval [tex][ -1, 0.5][/tex]
At [tex]x= -1[/tex] y- coordinate is equals to [tex]2[/tex]
At [tex]x= 0.5[/tex] y- coordinate is equals to [tex]2[/tex]
Local minimum [tex]= 1[/tex] at [tex]x=0[/tex]
Therefore, it is a correct option.
d. Over the interval [tex][0.5, 2],[/tex] the local minimum is [tex]4.[/tex]
In the given interval graph keeps on increasing [tex]1[/tex] to [tex]4[/tex] and so on.
It is not a correct option.
Hence, statement which is correctly identifies the local minimum of the graphed function is given by over the interval [tex][-1,0.5],[/tex] the local minimum is [tex]1[/tex].
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