Q. 9 - Calculus

Question

Given the following graph of f , graphically estimate the global extrema of f on each of the six intervals listed: 

$$\begin{gathered} \left(a\right) \left[0,4\right] \left(b\right) [2,5] \left(c\right) \left(-2,1\right) \\ \left(d\right) [0,\infty ) \left(e\right) (-\infty ,0] \left(f\right) \left(-\infty ,\infty \right) \end{gathered}$$

Step-by-Step Solution

Answer

Part (a) Minimum = 0  

Part (b) Minimum =  5     Maximum = 2

Part (c) Minimum = 0

Part (d) Minimum = 0 

Part (e) Minimum = 0  

Part (f) Minimum = 0  

Part (a) Step 1. Given information.

Given graph is :

 

We have to graphically estimate the global extrema of f on:

$$\begin{gathered} \left(a\right) \left[0,4\right] \left(b\right) [2,5] \left(c\right) \left(-2,1\right) \\ \left(d\right) [0,\infty ) \left(e\right) (-\infty ,0] \left(f\right) \left(-\infty ,\infty \right) \end{gathered}$$

Part (a) Step 2. Global extrema of f on [0,4].

It is seen that the function f has a global minimum at x=-0 as the function is decreased up to that point and the function f has no global maximum. 

Part (b) Step 1. Global extrema of f on [2,5].

It is seen that in between the [2,5]., the function f has a global minimum at x=5 as the function is decreases up to that point and the function f has a global maximum at x=2 as the function is increases to that point.

Part (c) Step 1. Global extrema of f on (-2,1).

It is seen that in between the (-2,1) , the function f has a global minimum at x=0 as the function is decreases up to that point and the function f has not a global maximum.

Part (d) Step 1. Global extrema of f on [ 0 , ∞ )

It is seen that in between the $[0,\infty )$, the function f has a global minimum at x=0 as the function is decreases up to that point and the function f does not have a global maximum.

Part (e) Step 1. Global extrema of f on ( - ∞ , 0 ] .

It is seen that in between the $(-\infty ,0]$, the function f has a global minimum at x=0 as the function is decreases up to that point and the function f does not have a global maximum.

Part (f) Step 1. Global extrema of f on - ∞ , ∞

It is seen that in between the $\left(-\infty ,\infty \right)$, the function f has a global minimum at x=0 as the function is decreases up to that point and the function f does not have a global maximum.