Answer:
There are in total 3 maximum and minimum points of f(x)
Step-by-step explanation:
To find the number of stationary points (maximum and minimum points) in any function (f(x)), we need to find for what values of x does the derivative of f(x) equal to 0.
mathematically, for how many values of x does f'(x) = 0
[tex]f'(x) = x(x-3)^2(x+1)^4[/tex]
[tex]0 = x(x-3)^2(x+1)^4[/tex]
since the factors can be separately solved we can write
[tex]0 = x, 0 = (x-3)^2, 0 = (x+1)^4[/tex]
[tex]x= 0, \sqrt{(x-3)^2} = \sqrt{0}, \sqrt{(x+1)^4}=\sqrt{0}[/tex]
[tex]x=0, (x-3)=0, (x+1)=0[/tex]
[tex]x = 0, x = 3, x = -1[/tex]
Since there are 3 answers of x for which f'(x) = 0, we can say that the there are a total of 3 stationary (maximum or minimum) points in f(x).
