Domain, intercetpts, vertical asymptote, horizontal asymptote
Find and classify all critical points
Find all intervals where the function is increasing or decreasing.
Find all intervals of concavity, and inflection points.
I did all the derivatives..
but i dunno what to do now.
i) f(x) = x(x^2+4)^2
f'(x) = (x^2+4)(5x^2+4)
f''(x) = 4x(5x^2+12)
ii) f(x) = x^(5/3) - 5x^(2/3)
f'(x) = 5/3*x(2/3) - 10/3*x^(-1/3)
f''(x) = 10/9*x^(-1/3) + 10/9*x(-4/3) for this one ii),
I have to care for cusps or vertical tangents..
iii) f(x) = 2cosx+sin2x
f'(x) = -2sin(x)+2cos(2x)
f''(x) = -2cos(x) - 4sin(2x) ==> is this right?
and for this one, I have to care about whether the function is periodic or not..