find the average rate of change
f(x)=x^2 + 2x between x=0 and x=6
can anyone please help me explain why the answer is 8?
thank you!
I assume you are not a calculus student.
avg rate= (f(6)-f(0))/(6-0)=(48-0)/6=8
nope im not :( and my teacher doesn't explain well...thank you! i've been trying to figure out how to come up with the asnwer but gosh i couldn't thank you again!
how did it become 48?
f(6) = 6^2 + 2(6) = 36+12 = 48
{{{(f(6) - f(0))/(6-0) = (6^2 + 2*6 - 0^2 - 2*0)/6 = 48/6 = 8}}}
To find the average rate of change of a function, you need to calculate the slope of the line connecting the two points on the graph corresponding to the given values of x.
In this case, we have the function f(x) = x^2 + 2x, and we want to find the average rate of change between x = 0 and x = 6.
Step 1: Find the value of f(x) at x = 0. Substitute x = 0 into the function:
f(0) = (0)^2 + 2(0) = 0 + 0 = 0.
Step 2: Find the value of f(x) at x = 6. Substitute x = 6 into the function:
f(6) = (6)^2 + 2(6) = 36 + 12 = 48.
Step 3: Calculate the average rate of change. The average rate of change is given by the formula: average rate of change = (f(x2) - f(x1)) / (x2 - x1), where x1 and x2 are the x-values corresponding to the given points.
Plugging in the values we found:
average rate of change = (f(6) - f(0)) / (6 - 0) = (48 - 0) / 6 = 8.
Therefore, the average rate of change of the function f(x) = x^2 + 2x between x = 0 and x = 6 is 8.