Given the function f(x)=-x^2-5x+12f(x)=−x 2 −5x+12, determine the average rate of change of the function over the interval -5\le x \le 4−5≤x≤4.

Given:

The function is

To find:

The average rate of change of the function over the interval −5 ≤ x ≤ 4.

Solution:

The average rate of change of a function f(x) over the interval [a,b] is

Putting x=-5 in the given function, we get

Putting x=4 in the given function, we get

Now, the average rate of change of the function over the interval −5 ≤ x ≤ 4 is

Therefore, the average rate of change of the function over the interval −5 ≤ x ≤ 4 is -4.

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

step-by-step explanation: