sketch a function that is continuous on (-∞,∞) and has the following properties. use a number line to…
sketch a function that is continuous on (-∞,∞) and has the following properties. use a number line to summarize information about the function. f(x)<0 on (-∞,-2); f(x)>0 on (-2,3); f(x)<0 on (3,∞). which of the following graphs matches the description of the given properties?
Answer
Explanation:
Step1: Analyze the sign of the derivative
The derivative $f'(x)<0$ on $(-\infty, - 2)$ means the function is decreasing on this interval.
Step2: Analyze the sign of the derivative
The derivative $f'(x)>0$ on $(-2,3)$ means the function is increasing on this interval.
Step3: Analyze the sign of the derivative
The derivative $f'(x)<0$ on $(3,\infty)$ means the function is decreasing on this interval.
Answer:
C.