The average rate of change from x =-2 to 1 is -7 and the equation of the secant line is y = -7x + 11
How to determine the average rate of change?
The function is given as:
g(x) = 7x^2 - 3
Calculate g(-2) and g(1)
g(-2) = 7(-2)^2 - 3 = 25
g(1) = 7(1)^2 - 3 = 4
The average rate is then calculated as:
[tex]m = \frac{g(-2) - g(1)}{-2 - 1}[/tex]
This gives
[tex]m = \frac{25 - 4}{-3}[/tex]
Evaluate
m = -7
Hence, the average rate of change from x =-2 to 1 is -7
The equation of the secant line
This is calculated using:
y = m(x -x1) + y1
So, we have:
y = -7(x + 2) + 25
Evaluate
y = -7x + 11
Hence, the equation of the secant line is y = -7x + 11
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