f(x)=2x^(3)–1x^(2)+3x–2
Find the average slope of this function on the interval (1,7).
Compute f(7) and f(1).
The average slope is
[f(7) - f(1)]/(7 - 1)
f(1) = 2 -1 +3 -2 = 2
f(7) = (2*343) - 49 + (3*7) - 2 = ?
To find the average slope of a function on a given interval, we need to calculate the slope between the two endpoints of the interval. In this case, we need to find the slope between the points (1, f(1)) and (7, f(7)).
First, let's find the values of f(1) and f(7) by substituting the x-values into the given function:
f(1) = 2(1)^(3) – 1(1)^(2) + 3(1) – 2
= 2(1) – 1(1) + 3(1) – 2
= 2 – 1 + 3 – 2
= 2
f(7) = 2(7)^(3) – 1(7)^(2) + 3(7) – 2
= 2(7) – 1(7) + 3(7) – 2
= 98 – 49 + 21 – 2
= 68
So, our two points are (1, 2) and (7, 68).
Next, we calculate the slope using the formula: slope = (y2 - y1) / (x2 - x1).
slope = (68 - 2) / (7 - 1)
= 66 / 6
= 11
Therefore, the average slope of the function on the interval (1, 7) is 11.