The following polynomial represents a profit function for a certain production line, where x is a number of produced units, find a. the zeros and the multiplicity of each b. where the graph crosses or touches the x-axis c. number of turning points d. explain the meaning of the above, if any f (x) = x^2 (x + 2)^3 (x^2 - 1)

Question

The following polynomial represents a profit function for a certain production line, where x is a number of produced units, find a. the zeros and the multiplicity of each b. where the graph crosses or touches the x-axis c. number of turning points d. explain the meaning of the above, if any  f (x) = x^2 (x + 2)^3 (x^2 - 1)

anonymous · Answer

$$f (x) = x^2 (x + 2)^3 (x^2 - 1)=f (x) = x^2 (x + 2)^3 (x+1)(x-1)$$
zeros are displayed for you
$$x^2=0\iff x=0$$ the mutiplicity is 2 because of the exponent
$$(x+2)^2=0\iff x=-2$$ and here the multiplicy is 3
$$x+1=0\iff x=-1$$
$$x-1=0\iff x=1$$ both have multiplicty 1

anonymous · Answer

oops typo 
$$(x+2)^3=0\iff x=-2$$ multiplicty is 3

anonymous · Answer

Thanks a bunch satellite 73

anonymous · Answer

By chance are you able to determine the number of turning point