well, first I factor it to see where zeros of the numerator and denominator are:
(2x+3)(x-4) / [ (3x-1)(x-2) ]
so you know the thing is going to be undefined at x = 1/3 and at x = 2
Now where are derivatives + , - and 0 ?
If you use this you get a graph
https://www.wolframalpha.com/input/?i=derivative+of+%28%282x^2-5x-12%29%2F%283x^2-7x%2B2%29
The derivative is
(x^2+80x-94) / [ (x-2)^2 (3x-1)^2]
note that the slope is infinite at x = 2 and at x = 1/3
You can see on the graph where the slope is + and where -
The derivative is zero when the numerator is 0 and that is your local max and min locations
Here is a root finder:
http://www.mathportal.org/calculators/polynomials-solvers/polynomial-roots-calculator.php
note the derivative is 0 at -40+/-11sqrt14 or about 1.16 and -81.2
Suppose that
f'(x)= (2x^2-5x-12)/(3x^2-7x+2) and that f(x) is continuous for all real numbers x.
a) Do a sign diagram to list the values of x where f(x) has local maximums and local minimums. In addition, list the intervals where f(x) is increasing and decreasing.
b) Draw the graph of some continuous function f(x) that has the properties you found in part a.
I need you to show your work for this problem so I can get better understanding and do the rest of my hw.
Thank you!
2 answers
good work, Damon, but we are give the derivative. The rational function is f'(x), not f(x).
1 answer