How do you find the average rate of change of $y = 4 x - 3 x^{2}$ $y=4x-3x^2$ over [2,3]?

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How do you find the average rate of change of $y = 4 x - 3 x^{2}$ $y=4x-3x^2$ over [2,3]?

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Answer 1 · 2017-09-11T18:35:57

$- 11$ $-11$

Explanation:

$the average rate of change of a function f(x) over an$ $"the average rate of change of a function f(x) over an "$
$interval between 2 points is the slope of the secant$ $"interval between 2 points is the slope of the "color(blue)"secant"$
$connecting the 2 points$ $"connecting the 2 points"$

$this is found using the following$ $"this is found using the following"$

$\frac{f (b) - f (a)}{b - a} \to [a, b]$ $(f(b)-f(a))/(b-a)to[a,b]$

$here [a, b] = [2, 3]$ $"here "[a,b]=[2,3]$

$\Rightarrow f (b) = f (3) = 12 - 27 = - 15$ $rArrf(b)=f(3)=12-27=-15$

$\Rightarrow f (a) = f (2) = 8 - 12 = - 4$ $rArrf(a)=f(2)=8-12=-4$

$average rate of change = \frac{- 15 - (- 4)}{3 - 2} = - 11$ $"average rate of change "=(-15-(-4))/(3-2)=-11$

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How do you find the average rate of change of $y = 4 x - 3 x^{2}$ $y=4x-3x^2$ over [2,3]?

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How do you find the average rate of change of $y = 4 x - 3 x^{2}$ $y=4x-3x^2$ over [2,3]?