the graph of ( y = f(x) ) is shown to the right. identify the ( x )-coordinates of the points where ( f(x) )…

the graph of ( y = f(x) ) is shown to the right. identify the ( x )-coordinates of the points where ( f(x) ) has a local maximum. which of the following shows every ( x )-coordinate where ( f(x) ) has a local maximum? choose the correct answer below. a. ( a,f,h ) b. ( b,e,g ) c. ( a,c,h ) d. ( c,f )

the graph of ( y = f(x) ) is shown to the right. identify the ( x )-coordinates of the points where ( f(x) ) has a local maximum. which of the following shows every ( x )-coordinate where ( f(x) ) has a local maximum? choose the correct answer below. a. ( a,f,h ) b. ( b,e,g ) c. ( a,c,h ) d. ( c,f )

Answer

Explanation:

Step1: Recall the definition of local maximum

A local maximum of a function (y = f(x)) occurs at a point (x = c) if (f(c)\geq f(x)) for all (x) in some open interval containing (c). Graphically, at a local maximum, the function changes from increasing to decreasing.

Step2: Analyze the given graph

Looking at the graph:

  • At point (x = a), the function is at an endpoint. Endpoints are not considered for local maxima (by the standard definition of local maxima which requires an open - interval around the point).
  • At point (x = c), the function changes from increasing (as we move from left to right towards (c)) to decreasing (as we move from left to right away from (c)).
  • At point (x = f), the function changes from increasing (as we move from left to right towards (f)) to decreasing (as we move from left to right away from (f)).
  • At point (x = h), it is an endpoint.
  • Points (b), (e), (g) are local minima (the function changes from decreasing to increasing at these points).

Answer:

D. (c,f)