Im having a little trouble on these questions, please help. I tried to figure out f prime of all then plug in the answers to get the max/mins then tried to figure out double prime to get the concavity and IP's, but im not sure if im going in the right diretion. Any help is greatly appreciated. Thanks.
1 Find the intervals of increase/decrease.
2 Find the local maximum and/or minimum values.
3 Find the intervals of concave up/concave down and the inflections points.
4 Use the information from parts (a)-(c) to sketch the graphs of the functions.
Functions
1. f(x) = 2sinx + cos(2x), [0 < x < 2π]
f prime (x) = 2cosx - 2sin(2x)
cosx = 0 = (π/2, 3π/2) sinx = 0 = (0,π,2π)
f double prime = -2sinx - 4cos(2x)
2. f(x) = (x^3-1)^2
f prime = 2(x^3-1)(3x) => 3x^2(x^3-1)
x= -1,1
fdouble prime = (3x^2)(3x) + (x^3-1)(6x) => 9x^3 + 6x^4 - 6x =>
3x(3x^2 + 2x^3 - 2)
3. f(x) = x^2 sqrt9-x^2 => x^2(9-x^2)^1/2
fprime = x^2 X 1/2(9-x^2)^-1/2 (-2x) + (9-x^2)^1/2 X (2x) => -2x^3(9/2-1/2^2)^-1/2 + (18x-2x^3)
4. f(x) = x^3+x / x^3+1
fprime = (x^3+1)(3x^2+1) - (x^3+x)(3x^2)/(x^3+1)^2