use the given information to make a good sketch of the function f(x) near x = 2. f(2)=4, f(2)= - 2…
use the given information to make a good sketch of the function f(x) near x = 2. f(2)=4, f(2)= - 2, inflection point at x = 2, f(x)>0 for x>2 choose the correct graph below.
Answer
Explanation:
Step1: Analyze function - value
The point ((2,4)) lies on the function since (f(2) = 4), so all graphs should pass through ((2,4)).
Step2: Analyze first - derivative
(f^{\prime}(2)=- 2), which means the slope of the tangent line to the function at (x = 2) is negative. Graphs B and D have positive slopes at (x = 2), so we can eliminate them.
Step3: Analyze second - derivative
There is an inflection point at (x = 2) and (f^{\prime\prime}(x)>0) for (x>2), which means the function is concave - up for (x > 2). Graph A is concave - down for (x>2), so we can eliminate it.
Answer:
C.