Monotonicity of Functions: Problems with Solutions

By Denitsa Dimitrova (Bulgaria)
Problem 1
Find the intervals on which the function
$f(x)=3x-3$ is increasing and decreasing.
Problem 2
Find the intervals on which the function
$f(x)=x^2-2x-3$ is increasing and decreasing.
Problem 3
Find the intervals on which the function
$f(x)=\sqrt{1-x}$ is increasing and decreasing
Problem 4
Find the intervals on which the function
$f(x)=x^3-6x^2+9x-12$ is increasing and decreasing
Problem 5
Find the intervals on which the function
$f(x)=-x^3+6x^2-9x$ is increasing.
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