sketch a graph of the function f that is continuous on (-oo,oo) and has the following properties. f(x)<0…
sketch a graph of the function f that is continuous on (-oo,oo) and has the following properties. f(x)<0, f(x)<0 choose the correct graph below. a. b. c. d.
Answer
Explanation:
Step1: Analyze first - derivative
Since (f^{\prime}(x)<0), the function (f(x)) is decreasing for all (x\in(-\infty,\infty)). This means that as (x) increases, (y = f(x)) decreases.
Step2: Analyze second - derivative
Since (f^{\prime\prime}(x)<0), the function (f(x)) is concave - down for all (x\in(-\infty,\infty)). A concave - down function has a graph that curves downward like an upside - down bowl.
Step3: Check the graphs
Graph A is increasing. Graph B is increasing. Graph C is decreasing and concave - down. Graph D is decreasing but concave - up.
Answer:
C.