Find Average Rate of Change

[nycmath]

Precalculus
Michael Sullivan
Edition 10
Chapter 2, Section 2.3

72. Find the average rate of change of f(x) = x^2 + 1 from -1 to 2.

[Eigenvalue]

We can use the average rate of change formula to find the average rate of change:
[tex]\frac{f(2)+f(-1)}{2-(-1)}[/tex]
=[tex]\frac{2²+1-(-1)²-1}{3}[/tex]
=[tex]\frac{5-2}{3}[/tex]
=1

[tex]\frac{f(x+h)-f(x)}{h}[/tex]
=[tex]\frac{(x+h)²+1-x²-1}{h}[/tex]
=[tex]\frac{2xh+h²}{h}[/tex]
=2x+h

[nycmath]

We can use the average rate of change formula to find the average rate of change:
[tex]\frac{f(2)+f(-1)}{2-(-1)}[/tex]
=[tex]\frac{2²+1-(-1)²-1}{3}[/tex]
=[tex]\frac{5-2}{3}[/tex]
=1

[tex]\frac{f(x+h)-f(x)}{h}[/tex]
=[tex]\frac{(x+h)²+1-x²-1}{h}[/tex]
=[tex]\frac{2xh+h²}{h}[/tex]
=2x+h

Yes. You got it right.