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The maximum value of the function is: 2 pi12.25The minimum value of the function is:pi/2-1-0.25On the interval (0, something/2), the function is: IncreasingDecreasingThe range of the function is:[-1, 1][-0.25, 2.25]All real numbers

The maximum value of the function is 2 pi1225The minimum value of the function ispi21025On the interval 0 something2 the function is IncreasingDecreasingThe ran class=

Respuesta :

Solution:

Given the trigonometric function:

[tex](x)=\frac{5}{4}\sin(x)+1[/tex]

we have

1) The maximum value of the function is

[tex]\begin{gathered} \frac{5}{4}+1=\frac{9}{4} \\ \Rightarrow2.25 \end{gathered}[/tex]

2) The minimum value of the function is

[tex]-0.25[/tex]

3) On the interval (0, π/2), the function is

[tex]Increasing[/tex]

4) The range of the function is

[tex][-0.25,\text{ 2.25\rbrack}[/tex]

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