B) g(x)=x^6-6x^5-21x^4© BrainMass Inc. brainmass.com October 17, 2018, 9:50 am 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.
Finding Maximum and Minimum Values
A) Find all critical points of f(x)=x^5+5x^4-35x^3 and classify each as a relative minimum, relative maximum or neither one.
B) Find the absolute maximum and minimum values of f(x)=2x^4-16x^3-32x^2 on the interval [-3,2].