Find the average rate of change for function f(x)=3x^(2)-5 at the points x[1]=6 and x[2]=10
avg rate of change is ∆y/∆x for the interval
∆y = f(10)-f(6) = 295-103 = 192
∆x = 10-6 = 4
avg rate of change is thus 192/4 = 48
To find the average rate of change for a function, we need to calculate the difference in the function values at the two given points, and then divide by the difference in the x-coordinates.
Let's first find the function values at the two points:
f(x[1]) = 3x[1]^2 - 5
= 3(6)^2 - 5
= 3(36) - 5
= 108 - 5
= 103
f(x[2]) = 3x[2]^2 - 5
= 3(10)^2 - 5
= 3(100) - 5
= 300 - 5
= 295
Now, let's calculate the difference in the function values:
f(x[2]) - f(x[1]) = 295 - 103
= 192
The difference in the x-coordinates is:
x[2] - x[1] = 10 - 6
= 4
Finally, we can calculate the average rate of change:
Average rate of change = (f(x[2]) - f(x[1])) / (x[2] - x[1])
= 192 / 4
= 48
Therefore, the average rate of change for function f(x)=3x^2-5 at the points x[1]=6 and x[2]=10 is 48.