Determine the intervals on which the following functions are increasing and decreasing and classify each of the critical points as a relative minimum, a relative maximum, or neither one.
B) g(x)=x^6-6x^5-21x^4© BrainMass Inc. brainmass.com June 20, 2018, 3:28 pm ad1c9bdddf
(1) f(x) = 3/4x^4 + 4x^3 + 6x^2 + 48
By taking the derivative, f'(x) = 3x^3 + 12x^2 + 12x = 3x(x^2 + 4x + 4) = 3x(x + 2)^2
Setting f'(x) = 0 to get two critical points: x = 0 or x = -2.
Hence, f(x) is increasing when x > 0 ...
In this solution we determine if the following functions are increasing of decreasing and classify each of the critical points as either relative minimum, maximum or neither.