Question

given the function ( f(x)=-4 x^{2}+5 x + 3 ).
find the average rate of change of ( f ) from ( x=-5 ) to ( x = 4 )
give your answer as an integer or reduced fraction.
average rate of change:

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \(y = f(x)\) from \(x=a\) to \(x = b\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a=-5\) and \(b = 4\).

Step2: Calculate \(f(-5)\)

Substitute \(x=-5\) into \(f(x)=-4x^{2}+5x + 3\).

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Step3: Calculate \(f(4)\)

Substitute \(x = 4\) into \(f(x)=-4x^{2}+5x + 3\).

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Step4: Calculate the average rate of change

Substitute \(f(-5)=-122\), \(f(4)=-41\), \(a=-5\), and \(b = 4\) into \(\frac{f(b)-f(a)}{b - a}\).

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Answer:

\(9\)