Let g(x) = 6x^2 - 8. Find the average rate of change from -8 to 5. Find an equation of the secant line containing (-8, g(-8)) and (5, g(5)). The average rate of change from -8 to 5 is .

Filipinacws

Filipinacws

Answered question

2022-08-06

Let 6 x 2 8
a) Find the average rate of change from -8 to 5.
b) Find an equation of the secant line containing (-8, g(-8)) and (5, g(5)).

Answer & Explanation

Isaias Archer

Isaias Archer

Beginner2022-08-07Added 11 answers

1. The average rate of change of g(x) over the interval [ -8, 5] is g ( 5 ) g ( 8 ) 5 ( 8 ) = 6 52 8 6 ( 8 ) 2 8 5 ( 8 ) = 150 8 384 + 8 13 = 234 13 = 18
2. A secant line is a straight line joining two points on a function. Here, the points are ( -8, g (-8)) and ( 5, g(5)) . Now g ( 8 ) = 6 ( 8 ) 2 8 = 6 64 8 = 384 8 = 376 and g ( 5 ) = 6 52 8 = 6 35 8 = 150 8 = 142. Thus, we are required to find the equation of the line connecting the points ( -8, 376) and ( 5, 142). Now, we know that the slope of the line joining the points ( x 1 , y 1 ) and ( x 2 , y 2 ) is y 2 y 1 x 2 x 1 . Thus, the slope of the required line is 376 142 8 5 = 234 13 = 18. We also know that the equation of the line joining the points ( x 1 , y 1 ) and ( x 2 , y 2 ) is y y 1 = m ( x x 1 ), where m is its slope. Finally, the equation of the required secant line is y 142 = 18 ( x 5 ) or y 142 = 18 x + 90, or y = 18 x + 90 + 142 , or y = 18 x + 232

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