Question 2: Given a function y=f(x) that has derivatives and is continuous on the set of real numbers R. Know the graph of the function y=f′(x) as shown below. In which of the following ranges does the function y=f(3x–9) covariate?

From the graph deduce:

\(\begin{array}{l} y’ = f’\left( x \right) < 0 \Leftrightarrow \left[\begin{array}{l}x<-1\\2

We have:

\(y = f(3x – 9) \Rightarrow y’ = 3.f'(3x – 9)\)

Inferred covariate function

\(\begin{array}{l} y’ > 0 \Leftrightarrow f'(3x – 9) > 0\\ y’ < 0 \Leftrightarrow f'(6 - 2x) > 0\\ \Leftrightarrow \left[\begin{array}{l}-1<3x-9<2\\3x-9>3\end{array}\right\Leftrightarrow\left[\begin{array}{l}\frac{8}{3}

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