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The function f(x)=2x^2+x+5 represents the number of jars of pickles, y in tens of jars, denise expects to sell x weeks after launching her online store. What is the average rate of change over the interval 1<\= x <\= 2? Pls help quick!

Sagot :

xKelvin

Answer:

The average rate of change is 7.

Step-by-step explanation:

We are given the function:

[tex]f(x)=2x^2+x+5[/tex]

Which represents the number of jars of pickles, y (in tens of jars), Denise expects to sell x weeks after launching her store.

We want to find the average rate of change over 1 ≤ x ≤ 2.

Essentially, we want to find the slope over f(1) and f(2).

Thus, first evaluate the two endpoints:

[tex]f(1)=2(1)^2+(1)+5=2+1+5=8[/tex]

And:

[tex]f(2)=2(2)^2+2+5=8+2+5=15[/tex]

This gives us the two points (1, 8) and (2, 15).

Then the average rate of change will be the slope between the two:

[tex]\displaystyle m=\frac{15-8}{2-1}=7[/tex]

With units, this means that over the first and second week, Denise sold on average 70 jars of pickles per week.

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