Let g(x) = 6x^2 - 3.

Question

(a) Find the average rate of change from -8 to 4.

(b) Find an equation of the secant line containing (-8, g(-8)) and (4, g(4)).

(a) The average rate of change from -8 to 4 is

Answer 1

a) The average rate of change measures how much a function changes on average over a given interval.

1. g(b) - g(a) / b - a
2. In this case b = 4 and a = -8.
3. g(4) = 6 (4)^2 - 3 = 93
4. g(-8) = 6 (-8)^2 - 3 = 381
5. When you plug these values into the first bullet point you will get a slope, m.

b) To find the equation of the secant line you need to know the slope, m, between the two points which is what you find in part a. Then you just plug in a point's values into the equation for point-slope form.

1. y - y1 = m ( x -x1)

Answer 2

Part a) The average rate of change can be calculated as the slope of the line between the two points. Therefore, we need to calculate g(-8) = 6*(-8)²-3 = 381 and g(4) = 6*4²-3 = 93 so the average rate of change is g(4) - g(-8) / 4 - (-8).

Part b) To find the equation of the secant line, use the slope you found in part a and the coordinates of one of the points in the point slope formula y - y₁ = m(x - x₁). Use (4, 93) and m = the answer from part a to complete.