Chapter 4.3, Problem 50E

(a)

To determine

To find: The sketch a possible graph for $f$ .

Explanation of Solution

Given information:

The given function is. $f\left(3\right)=2,f\text{'}\left(3\right)=\frac{1}{2}andf\text{'}\left(x\right)>0andf"\left(x\right)<0$ .

Graph:

Consider the graph is a function as shown in figure (1)

  

Figure-(1)

(b)

To determine

To find: The equation $f\left(x\right)=0$ .

Answer to Problem 50E

The equation $f\left(x\right)$ is constantly increasing and the function to decrease.

Explanation of Solution

Given information:

The given function is. $f\left(x\right)=x^3{\left(x-2\right)}^4$

Calculation:

Calculate the function

Therefore the equation $f\left(x\right)$ is constantly increasing and the function to decrease.

(c)

To determine

To find: The equation $f\text{'}\left(2\right)=\frac{1}{3}$ .

Answer to Problem 50E

The $f\text{'}\left(2\right)$ is constantly decreasing from left and right .

Explanation of Solution

Given information:

The given function is. $f\left(x\right)=x^3{\left(x-2\right)}^4$

Calculation:

Calculate the function

Therefore the $f\text{'}\left(2\right)$ is constantly decreasing from left and right .