Question

Find the average rate of change of g(x) = 3x³ + 1 from æ = - 1 to x = 4.

Answer 1

The average rate of change or the slope is found as 39.

What is the definition of line slope/ average rate of change?

• A line's slope is a measure of its steepness and orientation. The slope of a line can be calculated using any 2 different points on that line.
• The slope of a line formula calculates the ratio of "vertical change" to "horizontal change" between two distinct points on a line.
• The net change in y coordinates is Δy, while the net change in x coordinates is Δx.

The slope of the line is given by;

m = (y₂ - y₁)/(x₂ - x₁)

The function is given as;

g(x) = 3x³ + 1

The points are; -1 and 4.

Put x = -1

g(-1) = 3(-1)³ + 1

g(-1) = -2

Put x = 4

g(4) = 3(4)³ + 1

g(4) = 193

The points are;

(x₁ ,y₁) = (-1, -2)

(x₂, y₂) = (4, 193)

Put the values in the slope formula;

m = (193 + 2)/(4 + 1)

m = 195/5

m = 39

Thus, the value of the average rate of change is 39; which is also the slope of the function.

To know more about the slope of the line, here

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