Question

Hi,
I am lost on couple of problems and i was wondering if you could just help me out with them.

1. Find and classify the points of discontinuity of the function F(x) = (x^2+7x+12)/(x^3-9x)

now for this problem i know there is going to be an infinite discontinuity because of the asymptotes, but at what points? is it going to be at x=3 x=-3 x=0 OR since after factoring top and bottom the result is (x+4)/x(x-3) so is it going to be just x=0 x=3

Also, how does canceling after factoring affect the graph; does that mean there is going to be a hole (and a removable discontinuity)? I kind of forgot this from precalculus.


2. Find all points where the tangent line to y=x^3-6x+12 has slope -1.

-lost on this one


3. Use the table below, which shows values of f(x) for x near 2, to find the slope of a secant line that is an estimate for f '(2)
x 1.8 1.9 2.0 2.1 2.2
f(x) 2.24 2.27 2.30 2.33 2.37



4. F(x) = x^2 if x<1
4-kx if x >or equal to 1

For the value of k, is f(x) differentiable at x=1? explain your answer

got 3 for the value of k

Answer 1

Your chances of getting questions answered promptly, or at all, greatly improve if you post them one at a time. Many of the volunteers here do no have time to answer four questions of this complexity in one sitting.

Let's consider question #2:

The slope to the tangent line of a function f(x) is f'(x) = df/dx

Thus you want to know where
f'(x) = 3x^2 -6 = -1
3x^2 = 5
x = +or- sqrt(5/3)
= +1.291 or -1.291