Answer:
36
Step-by-step explanation:
3*3^2-3=3*9-3=24
3*9^2-3=243-3=240
(240-24)/6 = 36
The average rate of change f(x)=3x²-3 from 3 to 9 is 36.
The average rate of change is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.
The slope of the line connecting the two endpoints of a particular interval determines the average rate of change of a function (known as the secant line). Here is the formula for the average rate of change:
Average rate of change = ( y₂ - y₁ ) / ( x₂ - x₁ )
The function is given below.
f(x)=3x²-3
To calculate the average rate of change find f(3) and f(9).
f(3) = 3 x ( 3²) -3=( 3 x 9 ) -3=24
f (9) = 3 x ( 9² ) -3=243-3=240
The average rate of change will be calculated as:-
Average rate of change = [f(9) - f(3)] / [ 9 - 3 ]
= [ 240 - 24 ] / [ 6 ]
= 36
Therefore, the average rate of change is 36.
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