I don't understand these types of problems-
Find the average rate of change of f between 1 and x
f(x)-f(1)/x-1
and X cannot be equal to 1
1) f(x)= the square root of x+3
2) f(x)=1/(x^2)
3) f(x)=x^3 + x
Here's how you do #1. The others can be done the same way.
I will assume than f(x) = sqrt(x+3) and not (sqrt x) + 3. You should have used parentheses to clarify the problem.
Find the average rate of change of f between 1 and x . That is
[f(x)-f(1)]/(x-1)
= [sqrt(x+3) - sqrt4]/(x-1)
= [sqrt(x+3) - 2]/x-1)
is the average rate of change in this case, from 1 to x.
For x = 2, this is 0.236..
For x = 3, it is 0.224..
For x = 4, it is 0.215..
For x = 13, it is (4-2)/12 = 0.1667...
Need help I have 91.36 need to round it up to 5 whats my answer
To find the average rate of change of a function between two given values, you need to calculate the difference in function values divided by the difference in input values. Here's how you can find the average rate of change for each function:
1) First, substitute the function values into the formula: (f(x) - f(1))/(x - 1)
For f(x) = √(x + 3), substitute √(x + 3) for f(x) and simplify:
(√(x + 3) - √(1 + 3))/(x - 1)
2) For f(x) = 1/(x^2), substitute 1/(x^2) for f(x) and simplify:
(1/(x^2) - 1/(1^2))/(x - 1)
3) For f(x) = x^3 + x, substitute x^3 + x for f(x) and simplify:
((x^3 + x) - (1^3 + 1))/(x - 1)
Remember that x cannot equal 1, as specified in the problem.