End behavior, turning point, zeros and their multiplicity

The following will help you plot the graph and answer the questions about its characteristics.

Step-by-step explanation:

f(x) = x^3 - 10x^2 + 28x - 24

As the leading coefficient is 1 (positive) the graph will descend to the left and rise  to the right.

Relative maximum / minimum:

Find the derivative:

f'(x) = 3x^2 - 20x + 28 = 0   ( for  turning points).

(3x - 14 )(x - 2) = 0

x = 14/3 , 2.

The second derivative is  6x - 20.

When x = 14/3 second derivative is positive.

When x = 2 second derivative is negative

so x = 14/3 gives a relative minimum value for f(x)

and x = 2 gives a relative maximum.

If you plug these 2 values into f(x) you'll get  the corresponding values of f(x) and you can plot theses points.

The y-intercept is where x = 0 so it's the point (0, -24) so plot this as well.

If there is  one root which has multiplicity 2 then the graph will just touch the x-axis. This will be either one of the  above : relative  maximum or minimum.

no association

step-by-step explanation:

if you have eyes and you can use them efficiently you can see that it just looks like random dots like do a line of best fit and like they're so spread out it's such a weak association you might as well consider it nonexistent

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!