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Sagot :
The increasing interval of a function can be founded by taking the derivative of the function and then calculating where the derivative is possitive.
We have the function:
[tex]f(x)=(x-3)^2[/tex]The derivative, by the chain rule is:
[tex]f^{\prime}(x)=2(x-3)[/tex]Now we need to find the interval where the derivative is possitive. Let's find the root:
[tex]\begin{gathered} 0=2(x-3) \\ 0=x-3 \\ x=3 \end{gathered}[/tex]The derivative is 0 when x = 3. Now lets evaluate the derivative in a number greater than 3, if it's possitive, the increasing interval will be (3,∞) If it's negative, the interval will be (-∞, 3)
Let's evaluate for x = 4:
[tex]f^{\prime}(4)=2(4-3)=2[/tex]Then, the increasing interval is (3,∞)
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