Difference Quotient

[nycmathguy]

Section 1.4
Question 74

See attachment.

I need to find f(5) first.

f(5) = 5(5) - 5^2

f(5) = 25 - 25

f(5) = 0

I now need to find f(5 + h).

f(5 + h) = 5(5 + h) - (5 + h)^2

f(5 + h) = 25 + 25h - (25 + 10h + h^2)

f(5 + h) = 25 + 25h -25 -10h - h^2

f(5 + h) = 15h - h^2

We now have this:

[(15h - h^2) - 0]/h

(15h - h^2)/h

This simplifies to 15 - h.

What does 15 - h really mean? I know it's the difference quotient but what does that mean?

 

[MathLover1]

correct!

The difference quotient is a measure of the average rate of change of the function over an interval (in this case, an interval of h)

 

[nycmathguy]

correct!

The difference quotient is a measure of the average rate of change of the function over an interval (in this case, an interval of h)

Is rate of change a derivative?

 

[MathLover1]

yes

 

[nycmathguy]

yes

Cool. Wish I had more time to solve more daily questions.