Answer:
The average rate of change for the function over the given integral
Step-by-step explanation:
Explanation
<u>Average rate of a functio</u>n:-
<u>We can define the average rate of change of a function from a to b</u>
<u></u>
Given function f(x) = eˣ
Given interval x = a = -2 and y = b = 0
f(a) = f(-2) = e⁻²
f(b) = f(0) = e⁰
The average rate of change for the function over the given integral
Given problem: .
Solution: We can see that first we have 8 and 2 numbers in front of 10's powers.
So, we need to simplify 8 over 2 first.
If we divide 8 by 2, we get 4.
Now, let us work on 10's and their powers.
is being divided by
We can apply quotient rule of exponents remaining part.
According to quotient rule of exponents,
If we apply same rule, we need to subtract exponents of 10's.
If we simplify exponent part -4-(-2), it will give us -4+2 =-2.
So,
And final answer would be .
Using derivatives, it is found that the x-values in which the slope belong to the interval (-1,1) are in the following interval:
(-15,-10).
<h3>What is the slope of the tangent line to a function f(x) at point x = x0?</h3>It is given by the derivative at x = x0, that is:
.
In this problem, the function is:
Hence the derivative is:
For a slope of -1, we have that:
0.4x + 5 = -1
0.4x = -6
x = -15.
For a slope of 1, we have that:
0.4x + 5 = 1.
0.4x = -4
x = -10
Hence the interval is:
(-15,-10).
More can be learned about derivatives and tangent lines at brainly.com/question/8174665
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