Determine the net change and average rate of change between the values of the variable

Question

A function is given.

f(x) = 3 - 3x^2; x = 4, x = 4 + h

determine the net change between the given values of the variable.

determine the average rate of change between the given values of the variable.

Answer 1

Aaron, here's how to tackle this.

f(x) = 3 - 3 x²

⇒ f(4) = 3 - 3 (4²) = 3 - 45 = -45 . . . . . . . . . . . (1)

And f(4 + h) = 3 - 3 (4 + h)²

= 3 - 3(16 + 8h +h²)

= 3 - 48 - 24h -3h²

= -45 - 24h -3h² . . . . . . . . . . . . . . (2)

The net change, Δf = (-45 - 24h -3h²) - (-45) This is simply (2) - (1)

= -24h -3h²

And average change is Δf / h = (-24h -3h²⁾ / h

= -24 - 3h