Evaluate the function at the given value of the independent variable. Simplify the results.

Question

f(x)=x^3

 

(f(x+Δx)+f(x))/Δx  (Δx≠0)

Answer 1

I will use h in place of delta x simply because it's easier to type

 

((x+h)³ - x³)/h

 

= (x³ + 3x²h + 3xh² -x³)/h

 

= (3x²h + 3xh²)/h

 

= 3x² + 3xh

 

If you then take the limit as h --> 0, you will get 3x².