Find the change of fx x2 5 from 3 to 6 Given that fx 3x2

Find the change of f(x)= x^2 + 5 from -3 to 6 Given that f(x) = 3x^2 - 2x + 5, find f(x+h) - f(x)/h. Simplify your answer.

Solution

f(x) = x^2 + 5

change from -3 to 6

applying rate of change formula f(b) - f(a) / b-a

f(6) = 6^2 + 5 = 41

f(-3) = (-3)^2 + 5 = 14

rate of change = 41 - 14 / 6-(-3) = 27/9 = 3

rate of change = 3

2) f(x) = 3x^2 - 2x + 5

f(x+h) = 3(x+h)^2 - 2(x+h) + 5 = 3 (x^2 + 2xh + h^2) - 2x - 2h + 5

f(x+h) = 3x^2 + 6xh + 3h^2 - 2x - 2h + 5

f(x+h) - f(x) / h = {3x^2 + 6xh + 3h^2 - 2x - 2h + 5 - 3x^2 + 2x - 5 }/ h

we are left with

{6xh + 3h^2 - 2h }/ h

on dividing we get

6x + 3h - 2