Which Interval For The Graphed Function Contains The Local Maximum?

Which Interval For The Graphed Function Contains The Local Maximum?

A. [–3, –2]

B. [0, 2]

C. [–2, 0]

D.[2, 4]

Answer: B. [0, 2]

Local maximum is the highest value that a function can attain in a particular interval even though the function’s maximum in that interval may not necessarily be the global maximum. In this case, the interval of the graphed function is [0, 2] which contains the highest point of the graph. This means that within this range the function is at its maximum value and then decreases on either side of the range. It is always very essential to learn about the local maximum to interpret the behaviour of a function and is relevant in different areas of practice. For example, in finance, there is the benefit of finding the local maximum when calculating maximum stock prices in the period in question. In physics, the energy or force of a system is described by local maxima as being the highest point that has been so far reached. Thus, to find the local maximum of the given function, we meet within the interval and look for the point that gives the maximum value of the function which continues to decrease on both ends. There is, however, a need to distinguish between the local maximum and the global maximum which is the maximum value considering all values of x. This knowledge allows one to understand some properties of the function in the given range and its change concerning the range containing the local maximum. This information is most helpful in optimization problems and in cases involving analysis of real-life situations which can be expressed mathematically.