Consider the following function. (If an answer does not exist, enter DNE.) f(x) = 1 + 7/x − 4/x^2

Question

(a) Find the vertical and horizontal asymptote(s). (Enter your answers as a comma-separated list.)

(b) Find the interval where the function is increasing and decreasing. (Enter your answer using interval notation.) 

(c) Find the local maximum and minimum values. 

(d) Find the interval where the function is concave up and down. (Enter your answer using interval notation.) 

Find the inflection point.

Answer 1

This would be easier if you write the function a one fraction

f(x) = (x² + 7x - 4)/(x²)

(a) VA occur when the denominator = 0, HA occur is a little trickier. you need to compare the degree of the numberator and denominator. in this problem the degrees are equal, so the HA is at Y = (leading coefficientof numerator/leading coefficient of denominator) or y=1/1 which means the HA is y = 1

(b) to find increasing and decreasing find the derivative of the function. If the derivative is + the function is increasing, if the derivative is - the functions is decreasing.

The remaining questions all involve finding derivatives. Try them and contact me if you need further help. It may be helpful for you to find some tutoring. if you are interested, I have helped many students with these types of problems. Contact me here on Wyzant.