se the table below of the function f(x) = x4  − 2x3  to answer this question: xf(x)−13001−120327what is the average rate of change from x = −1 to x = 2?

The average rate of change from x=-1 to x=2 is -1

Solution:

f(x)=x^4-2x^3

x   f(x)

-1    3

0    0

1     -1

2    0

3   27

Average rate of change from x=-1 to x=2: r=?

Average rate of change from x=a to x=b: r=[f(b)-f(a)]/(b-a); a=-1, b=2

a=-1→f(a)=f(-1)=3 See table

b=2→f(b)=f(2)=0 See table

Replacing the values in the formula:

r=(0-3)/(2-(-1))

r=(-3)/(2+1)

r=(-3)/(3)

r=-1

The average rate of change from x=-1 to x=2 is -1

i used to know but i learned it a long time ago sorry

step-by-step explanation:

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.