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What is the average rate of change of the function over the interval x = 0 to x = 4?

f(x)= 2x−1 3x+5 f(x)=2x−13x+5

Enter your answer, as a fraction, in the box.

Respuesta :

sarkhan2018
Applying the formula for the average change of function [tex]A(x)= \frac{f(x)-f(a)}{x-a} [/tex], we can solve this problem considering that x=4 and a=0. Then, f(4)=2*4-13*4+5=-39 and f(0)=2*0-13*0+5=5, Then [tex]A(x)= \frac{-39-5}{4-0} = -9.75[/tex]

Answer:

Average rate of change of function is [tex]\frac{61}{400}[/tex].

Step-by-step explanation:

Given Function: [tex]f(x)=\frac{2x-1}{3x+5}[/tex]

To find: Average rate of change of function over interval of x = 0 to x = 4.

We use the the following formula to find the average rate of change of function f(x) over interval x= a and x = b

[tex]Average\:rate\:of\:change\:of\:function=\frac{f(b)-f(a)}{b-a}[/tex]

here, a = 0 and b = 4

We find value of f(4) ande f(0)by putting x = 4,

[tex]f(4)=\frac{2\times4-1}{3\times4+5}=\frac{8-1}{12+5}=\frac{7}{17}=0.41[/tex]

[tex]f(0)=\frac{2\times0-1}{3\times0+5}=\frac{-1}{5}=-0.2[/tex]

So,

[tex]Average\:rate\:of\:change\:of\:function=\frac{f(4)-f(0)}{4-0}=\frac{0.41-(-0.2)}{4}=\frac{0.41+0.2}{4}=\frac{0.61}{4}=\frac{61}{400}[/tex]

Therefore, Average rate of change of function is [tex]\frac{61}{400}[/tex].

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