# calculus

posted by .

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

• calculus (#2of 4) -

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

## Similar Questions

1. ### algebra

Find the points of discontinuity and any holes. y=x^2-1/(x^2+3x+2) please and thank you y =(x^2-1)/((x+1)(x+2)) =(x-1)/(x+2) we cancelled the (x+1)/(x+1) which is 0/0 for x=-1 so in our simplified expression when x=-1 y = -2 There …
2. ### math

Which of the following functions f has a removable discontinuity at a?
4. ### Calculus

A function f(x) is said to have a removable discontinuity at x=a if: 1. f is either not defined or not continuous at x=a. 2. f(a) could either be defined or redefined so that the new function IS continuous at x=a. -------------------------------------------------------------------------------- …
5. ### Calculus

A function f(x) is said to have a removable discontinuity at x=a if: 1. f is either not defined or not continuous at x=a. 2. f(a) could either be defined or redefined so that the new function IS continuous at x=a. -------------------------------------------------------------------------------- …
6. ### calculus

Find the discontinuities of the given function. Classify them as a point discontinuity or a jump discontunuity. g(x)= x, x<-3 5x/(x^2-4x), x>= -3
7. ### Calculus (Discontinuities)

Suppose, f(x) = { (x - 1)^2 / x + 1 if x < 2 (x^2 - 2x - 8)/(x - 4) if 2 </= x < 4 (1 / (x - 3)) + 5) if 4 </= x Identify any points of discontinuity, and determine (giving reasons) if they are removable, infinite, or jump …
8. ### Calculus (Discontinuity)

Suppose f(x) = [sin(x^2 - 4)]^ -1. Identify any points of discontinuity, and determine (giving reasons) if they are removable, infinite, or jump discontinuities. Okay, I presume that the [ ] brackets denote the greatest integer function …
9. ### Calculus Find max and min and saddle

Find and classify all local min and maxima and saddle points of the function f(x,y)=/3yx^2-3xy^2+36xy I know there are 3 saddle points and one maxima. This is what I got: D=FxxFyy-(Fxy)^2 = 36xy-36(x+y-6)^2 But how do i solve for zero?
10. ### Calculus

Let f(x)=|x+1|/(x^(2)-1). Is f continuous?

More Similar Questions