From the given equation,
[tex]y=5x^2+2[/tex]Now,
For find the maximum and minimum value of the function,
The maximum and minimum of the function is,
[tex]\begin{gathered} y=5x^2+2 \\ x=-\frac{b}{2a} \\ =-\frac{0}{2\times5} \\ =0 \end{gathered}[/tex]Then,
Put the value of x into the given equation to find the value of y,
So;
[tex]\begin{gathered} y=5(0)^2+2 \\ y=0+2 \\ y=2 \end{gathered}[/tex]Hence, the maximum and minimum function is,
(0, 2).
Now,
The domain of the given funcytion is,
[tex](-\infty,\text{ }\infty)[/tex]And,
The range of the given function is,
[tex]\begin{gathered} y=5x^2+2 \\ f(x)\ge2 \end{gathered}[/tex]So,
The range of function is,
[tex]\lbrack2,\text{ }\infty)[/tex]The increasing and decreasing of the function is,
[tex]\begin{gathered} \text{Increasing:- }(0,\text{ }\infty) \\ \text{Decreasing:- }(-\infty,\text{ 0)} \end{gathered}[/tex]