Intervals of Function Increase or Decrease

==2024-12-14

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Think about the perspective not the implication.

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Theory

A function $f(x)$ increases at a given interval $(a,b)$ if $\forall x_o\in (a,b)$, $f^{\prime }(x_o)>0$.

That means, at that interval, when $x$ increases, $y$ increases as well because of the positive slope of the curve.

Similarly, if $f^{\prime }(x_o)>0$, the function is decreasing at that interval due to the negative slope of the curve.

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PTR