write out an expression for the average rate of change of f(x) from x=-5 to x=5

Answer 1

Sara,

"Average rate of change" is an important concept in Calculus, but it is something you learn earlier on in Algebra! Your question may seem confusing given the limited amount of information but it is simply asking for the slope formula of an expression between two given points X₁ = -5 and X₂ = 5. This can be understood as the "rise" of the Y values, or the f(X), divided by the "run" of the X values. In other words:

Standard form:

[f(X₂) - f(X₁)]/[(X₂) - f(X₁)]

Or in the case of our given X values:

[f(5) - f(-5)]/[(5) - (-5)]

Simplified further:

[f(5) - f(-5)] / 10

This can be thought of the equation f(X) evaluated at X = 5 minus the value of the same equation evaluated at X = -5, all divided by 10.

Thanks!