given the graph of the function f below, determine all intervals on the open interval (-9, 9) where f(x) ≥ 0…
given the graph of the function f below, determine all intervals on the open interval (-9, 9) where f(x) ≥ 0 and f(x) ≥ 0. f(-8.5)= -2.0626
Answer
Explanation:
Step1: Recall the meaning of $f^{\prime}(x)\geq0$
$f^{\prime}(x)\geq0$ means the function is non - decreasing. Visually, the graph is going up or is horizontal.
Step2: Recall the meaning of $f(x)\geq0$
$f(x)\geq0$ means the function values are non - negative. Visually, the graph is above or on the $x$ - axis.
Step3: Analyze the graph
By looking at the graph of $y = f(x)$ on the open interval $(-9,9)$:
- We find the intervals where the graph is rising (non - decreasing, $f^{\prime}(x)\geq0$) and also above or on the $x$ - axis ($f(x)\geq0$).
- The function is non - decreasing and non - negative on the interval $[6,9)$.
Answer:
$[6,9)$