I need more Calculus help!

all but the last one can be solved by taking derivatives and setting them equal to zero. Lhospitals rule is pretty straight forward. Take the derivative of just the numerator and then just the denominator. Repeat this until the problem is evaluatable. I suggest the site mathworld for additional guidance. the site matheolrd

Perhaps you should either see the professor or drop the course. Having the math mavens here do your homework only benefits them. And why continue to torture yourself?

Your earlier plea for help

Sorry I wish I could help I know how you feel I’m in calculus right now and it really blows

That’s easy…

1. Take the first derivative of the function. On this one you will have to use quotient rule: (u’v -v’u)/(v^2), set it equal to 0. Evaluate the derivative at a point smaller than your 0 value, if f(2)=0, then do something like f’(1) = y and f’(3) = y. This will tell you if the function is increasing or decreasing. If your evaluation of f’(x) is negative, then the function is decreasing at that point. If your evaluation of f’(x) is positive then the function is increasing at that point.

Your local maximum and minimums are found by finding where the function is increasing and decreasing. if you evaluate points on either side of the function where it’s 0, and the signs change, then that is a local min or max. If the signs don’t change, then you have a horizontal line of inflection.

To find whether the function’s concavity, you need to take the second derivative of the function, put simply take the derivative of the derivative you got just before. Set the second derivative = 0 and solve for x. Like min/max, evaluate points on either side of the zeroes. If the evaluations are negative, then the function is concave up, conversely if the evaluations are positive, the function is concave down. Your points of inflection are the values of x when you solved for x in the first derivative.

2&3. Evaluate the function at t=1. If you get 0/0, ∞/∞ or 0•∞, then you use l’Hopital’s rule. Since the function is already set up as a rational function, all you do is take the derivatives of the numerator and denominator. Evaluate the function at t=1. What you’ll get is either the limit at t=1 or 0/0, etc. If your function is still undefined at t=1, then you need to take the second derivative of the function until you get a value where the function is undefined. If you take derivatives until you have a constant, then the limit at t=1 does not exist. On 3, you need to get it into a form where you have a numerator and denominator which when the function is undefined at t as described above. Once you get it into that form, just take derivatives and evaluate at t=1.