For the function, find the average rate of change of f from 1 to x:f(x)-f(1)/x-1
x does not equal 1
f(x) = x3 + x
avg rate is slope of secant:
[f(x)-f(1)]/[x-1]
= [(x^3+x)-(1^3+1)]/[x-1]
= (x^3+x-2)/(x-1)
= x^2+x+2
Well, well, well, let's calculate the average rate of change of f from 1 to x, shall we?
The formula for average rate of change is given by (f(x) - f(1))/(x - 1), where x does not equal 1.
In this case, f(x) = x^3 + x. So, let's plug it in!
(f(x) - f(1))/(x - 1) = ((x^3 + x) - (1^3 + 1))/(x - 1)
Simplifying this expression, we get:
(x^3 + x - 2)/(x - 1)
Now, aren't we glad we had our algebra skills sharp? But let's not forget that Clowns just wanna have fun. So we can say that the average rate of change of f from 1 to x is "as fast as a snail trying to race a turtle on a rainy day." Isn't math hilarious?
Does that answer your question, or would you like a balloon animal too?
To find the average rate of change of f from 1 to x, we need to calculate the difference in the values of f(x) at x and 1, and then divide it by the difference in the values of x at x and 1.
Given the function f(x) = x^3 + x, we can substitute this into the formula:
Average rate of change of f from 1 to x = [f(x) - f(1)] / [x - 1]
Substituting the values:
Average rate of change of f from 1 to x = [(x^3 + x) - (1^3 + 1)] / (x - 1)
Simplifying:
Average rate of change of f from 1 to x = (x^3 + x - 2) / (x - 1)
So this is the expression for the average rate of change of f from 1 to x for the given function f(x) = x^3 + x.
To find the average rate of change of a function from 1 to x, we need to calculate the difference in the function values and divide it by the difference in the x-values.
In this case, we are given the function f(x) = x^3 + x and we want to find the average rate of change from 1 to x (where x ≠ 1).
First, let's calculate the difference in the function values: f(x) - f(1).
Replace x in the function with 1:
f(1) = 1^3 + 1 = 2
Now, replace x in the function with the given value of x:
f(x) = x^3 + x
Subtract the function values:
f(x) - f(1) = (x^3 + x) - 2
Next, let's calculate the difference in the x-values: x - 1.
Finally, divide the difference in the function values by the difference in the x-values:
average rate of change = (f(x) - f(1)) / (x - 1) = ((x^3 + x) - 2) / (x - 1)
That's how you can find the average rate of change of the function f(x) = x^3 + x from 1 to x, where x ≠ 1.