calculus for business

Question

USE THE FOUR-STEP PROCESS TO FIND F¹(X) AND THEN FIND F¹(2), F¹(4), AND F¹(6).

F(X) = 18√x+3

Answer 1

Using the 4 step process

Step 1:

F(x+h) = 18√(x+h) + 3

F(x) = 18√x + 3

Step 2:

F(x+h) - F(x) = 18√(x+h) +3 - (18√x +3) = 18(√(x+h) - √x)

Multiply by 1 = (√(x+h) + √x)/ (√(x+h) + √x) which won't change the expression.

Remember that (a-b)(a+b) = a^2-b²

This gives

18(x+h -x)/(√(x+h) + √x) = 18h//(√(x+h) + √x)

Step 3:

Divide by h and simplifying

18h/(h(√(x+h) + √x)) = 18/√(x+h) + √x)

F'(x) = lim 18/√(x+h) + √x)

h→0

Step 4:

Compute the limit as h→0

F'(x) = lim 18/√(x+h) + √x) = 18/(√x + √x) = 18/(2√x) = 9/√x

h→0

---

F'(1) = 9/√1 = 9

F'(4) = 9/√4 = 9/2

F'(6) = 9/√6 = (9√6)/6 = (3√6)/2