Hi. First of all you need to know that to find information reguarding max/min and inc/dec - you will need the first derivative. Then to find the critical points that you will test, set the first derivative = 0 and/or find where the first derivative is undefined (this may be why you are asked about asymptotes). After finding the critical points - whenever the first derivative is positive, the function is increasing. Whenever the derivative is negative, the function is decreasing. The max occurs when the derivative changes signs from positive to negative. The min occurs when the derivative changes from negative to positive. This is because the first derivative is describing the slope of the function. For example, 1) the first derivative is: 15x^4 + 20x^3 = 0. To solve, factor: 5x^3(3x + 4) = 0 which leads you to x=0 and x=-4/3. Now check the sign (+ or -) before and after each value. A lot of people organize this on a number line or chart.
To get the points of inflection and the concavity: use the second derivative. To find points of inflections, set the second derivative = 0 or where it is undefined. Then do the same sign test. If the second derivative is positive, the function is concave up in that interval. If the second derivative is negative, the function is concave down in that interval. If there is any kind of a sign change, then that x value is where there is a point of inflection (which is where the concavity changes).
1) Second derivative: 60x^3 + 60x^2 = 0, factor: 60x^2(x+1)=0 yields x=0 and x=-1. Now check your signs.
For problem 2 - you need to use the product rule. For problem 3 - you need to use the quotient rule.