Question

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.

Answer 1

Given:

The equation is,

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

To find: The average rate of change

Step-by-step explanation:

The average rate of the change formula is,

`A\left(x\right)=(f\mleft(b\mright)-f\mleft(a\mright))/(b-a)`

Here, we have

`\begin{gathered} a=2 \\ b=4 \end{gathered}`

Substituting we get,

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

Final answer:

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