Question

Use the 4 step process to find the f'(x) of the function f(x)=x^2-3/2

Answer 1

see below

Explanation:

Modified problem

(x)^2-3/x

Step 1: Find f(x+h)

(x+h)^2-3/(x+h)

x^2 +2hx + h^2 -3/(x+h)

Step 2: Find f(x + h) − f(x)

x^2 +2hx + h^2 -3/(x+h) - ( x^2-3/x)

Distribute the minus sign

x^2 +2hx + h^2 -3/(x+h) - x^2+3/x

Combine like terms and get a common denominator

2hx + h^2 -3x/(x(x+h)) +3(x+h)/(x(x+h)

2hx + h^2 +3h/(x(x+h))

Step 3: Find (f(x + h) − f(x))/h

(2hx + h^2+3h/(x(x+h)) )/h

2hx/h + h^2/h+3h/(x(x+h)) /h

2x +h +3/(x(x+h))

Step 4: Find lim h→0 (f(x + h) − f(x))/h

2x+0 +3/(x(x+0))

2x +3/x^2