Find the slope of the line secant to the following function passing through the given x-values:
f(x) = x3 + 5x; x = 3 and x = 6
If f(x)=x^3+5x
then f(3)=27+15=42, f(6)=216+36=252
and slope=(252-42)/(6-3)
To find the slope of the line secant to the function passing through the given x-values, we need to find the average rate of change of the function over that interval. The average rate of change is equal to the slope of the secant line.
First, let's find the values of the function at the x-values given.
For x = 3:
f(3) = 33 + 5(3) = 27 + 15 = 42
For x = 6:
f(6) = 63 + 5(6) = 216 + 30 = 246
So, the y-values corresponding to x = 3 and x = 6 are 42 and 246, respectively.
Now, we can calculate the slope:
Slope = (change in y) / (change in x)
= (246 - 42) / (6 - 3)
= 204 / 3
= 68
Therefore, the slope of the line secant to the function passing through x = 3 and x = 6 is 68.