What are the values and types of the critical points, if any, of #f(x)=(2x^2+5x+5)/(x+1)#?
critical points are 0, -2, -1
Minima at (0,5), Maxima at (-2,-3), Discontinuous at x=-1
critical points are those at which f'(x) is =0, or for which f'(x) is not defined.
In this case f'(x)=
Critical points are therefore x=0, x=-2 and x= -1
For determining the types find f"(x)=
For x=0, f"(x) would be +ive, hence it is a minima at the point (0, 5)
For x= -2, f"(x) would be -ive, hence it is a maxima at the point (-2,-3)
At x=-1, f(x) does not exist. x=-1 is a vertical asymptote