Question

Find the intervals of increase and decrease of $f\left(x\right)=-0.5x^2+1.1x-2.3$

• A. $f$ increases $(-\infty ,1.1)$
• B. $f$ increases $(1.1,+\infty )$
• C. $f$ decreases $(-\infty ,1.1)$
  
• D. $f$ decreases $(1.1,+\infty )$

Answer 1

Answer: (A), (D)

$f$ increases $(-\infty ,1.1)$
$f$ decreases $(1.1,+\infty )$

Given: $f\left(x\right)=-0.5x^2+1.1x-2.3$

Differentiating both sides

$f^{\prime }\left(x\right)=-x+1.1$

$f^{\prime }\left(x\right)>0$ for $x<1.1$

So, increasing for $x\in (-\infty ,1.1)$

and decreasing for $x\in (1.1,\infty )$