Hi, I'm stuck on my calculus problem which is due tonight.
Here's the full question,
Q. For the following functions, do a full analysis of the function itself, the first derivative, and the second derivative.
Provide information about the
- domain, intercepts, and vertical and horizontal asymptotes.
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) 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..
Please math people.. help me.. I'm a newb