How do you solve this problem? Which is the right answer and why?
a. An absolute maximum
b. An absolute minimum
c. A critical point but not an extremum
d. Not a critical point
e. none of these
How do you solve this problem? Which is the right answer and why?
a. An absolute maximum
b. An absolute minimum
c. A critical point but not an extremum
d. Not a critical point
e. none of these
Differentiation gives f'(x) = 3(x+2)^{2}^{ }which is 0 at x = -2. Therefore this is a critical point. Notice that the derivative is positive everywhere else. Therefore this point is not an extremum. So the answer is c.
I agree with Roman using and his differentiation, however, this is not a Calculus question. From Algebra 1, f(x) is in the form of y = x^3 which passes through the point (0,0) and changes the instantaneous slope from positive to negative, it is a point of inflection.
As expressed f(x) = (x+2)^3 - 4 tells us the translation of the y = x^3 graph with its inflection point of (0,0) to a new inflection point of (-2,-4). c. a critical point but not an extremium