Consider the following expressions as functions of a with domain equal to the open interval (0, 1) and codomain equal to R. Which one of these functions is bounded and attains an absolute maximum but does not attain an absolute minimum? sin(x) ○ cos(x) ○ 1/x

Find the intervals where the function concaves up and down for f(x) = 8 sin(x) + cot(x),    −π ≤ x ≤ π

function, that is 0 everywhere except at t=0, is know as:

1) Consider f(x) = 3x4 -8x³ +6 a) Find all critical points of the function (make sure to consider if the derivative is defined everywhere or not!). Label them in increasing order, 21, 22, 23, etc (for how many you find). b) Use the first derivative test to determine if x₁ is a local max, min, or neither. Find the y value associated with this a value and write it as a point (x, y). 1 c) Use the second derivative test to determine if x2 is a local max, min, or neither. Find the y value associated with this a value and write it as a point (x, y).