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.

the answer is the third / last answer

step-by-step explanation:

a - base

b - exponent

so,