(-1,0) (-1,3) Find the rate

Mathematics

1 answer:

Eduardwww [97]3 years ago

3 0

Answer:

The answer is 3/0, which is undefined/∞

Step-by-step explanation:

3-0=3

-1+1=0

3/0= undefined or ∞

You might be interested in

The graph of F ( x ) = 4/x2 - 2x - 3 is shown <br> for which values of X is f ( x ) decreasing

Elza [17]

Hi there!

$\large\boxed{(-\infty, \sqrt[3]{-4}) \text{ and } (0, \infty) }$

We can find the values of x for which f(x) is decreasing by finding the derivative of f(x):

$f(x) = \frac{4}{x^2} - 2x - 3$

Taking the derivative gets:

$f'(x) = -\frac{8}{x^3} - 2$

Find the values for which f'(x) < 0 (less than 0, so f(x) decreasing):

0 = -8/x³ - 2

2 = -8/x³

2x³ = -8

x³ = -4

$x = \sqrt[3]{-4}$

Another critical point is also where the graph has an asymptote (undefined), so at x = 0.

Plug in points into the equation for f'(x) on both sides of each x value to find the intervals for which the graph is less than 0:

f'(1) = -8/1 - 2 = -10 < 0

f'(-1) = -8/(-1) - 2 = 6 > 0

f'(-2) = -8/-8 - 2 = -1 < 0

Thus, the values of x are:

$(-\infty, \sqrt[3]{-4}) \text{ and } (0, \infty)$

6 0

3 years ago

the change in water vapor in a cloud is modeled by a polynomial function, c (x). describe how to find the x - intercepts of c (x

lukranit [14]

The change in the water vapors is modeled by the polynomial function c(x). In order to find the x-intercepts of a polynomial we set it equal to zero and solve for the values of x. The resulting values of x are the x-intercepts of the polynomial.

Once we have the x-intercepts we know the points where the graph crosses the x-axes. From the degree of the polynomial we can visualize the end behavior of the graph and using the values of maxima and minima a rough sketch can be plotted.

Let the polynomial function be c(x) = x ² -7x + 10

To find the x-intercepts we set the polynomial equal to zero and solve for x as shown below:

x ² -7x + 10 = 0

Factorizing the middle term, we get:

x ² - 2x - 5x + 10 = 0

x(x - 2) - 5(x - 2) =0

(x - 2)(x - 5)=0

x - 2 = 0 ⇒ x=2

x - 5 = 0 ⇒ x=5

Thus the x-intercept of our polynomial are 2 and 5. Since the polynomial is of degree 2 and has positive leading coefficient, its shape will be a parabola opening in upward direction. The graph will have a minimum point but no maximum if the domain is not specified. The minimum points occurs at the midpoint of the two x-intercepts. So the minimum point will occur at x=3.5. Using x=3.5 the value of the minimum point can be found. Using all this data a rough sketch of the polynomial can be constructed. The figure attached below shows the graph of our polynomial.