Find the different quotient f (x+h) - f (x) / h given the function of f (x) = 3x^2+2

This is 6x.

Step-by-step explanation:

f (x) = 3x^2 + 2

The differential coefficient (f' (x)) is the limit as h-->0 of [ f (x+h) - f (x) ] / h.

f' (x) = [3 (x + h) ^2 + 2 - (3x^2 + 2) ] / h

= (3x^2 + 6hx + 3h^2 + 2 - 3x^2 - 2) / h

= (6hx + 3h^2) / h

= 6x + 3h

As h approaches very close to 0 we can neglect the 3h.

so f' (x) = 6x (answer).