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What is the average rate of change of the equation f(x)^2+3x-5 from x=2 to x=4?Type your numerical answer below. Use the hyphen (-) to represent a negative sign if necessary.

What Is The Average Rate Of Change Of The Equation Fx23x5 From X2 To X4Type Your Numerical Answer Below Use The Hyphen To Represent A Negative Sign If Necessary class=

Sagot :

Given:

The equation is,

[tex]f\mleft(x\mright)=x^2+3x-5,x=2\text{ to x = 4}[/tex]

To find: The average rate of change

Explanation:

The average rate of the change formula is,

[tex]A\left(x\right)=\frac{f\mleft(b\mright)-f\mleft(a\mright)}{b-a}[/tex]

Here, we have

[tex]\begin{gathered} a=2 \\ b=4 \end{gathered}[/tex]

Substituting we get,

[tex]\begin{gathered} A\lparen x)=\frac{f\mleft(4\mright)-f\mleft(2\mright)}{4-2} \\ =\frac{\left\lbrack4^2+3\left(4\right)-5\right?-\left\lbrack2^2+3\left(2\right)-5\right?}{2} \\ =\frac{16+12-5-\left\lbrack4+6-5\right\rbrack}{2} \\ =\frac{23-5}{2} \\ =\frac{18}{2} \\ =9 \end{gathered}[/tex]

Final answer:

The average rate of change of the given equation is 9.

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