Find and simplify the difference quotients f (6+h) - f (6)

f (x) = 15x² + 6

180h + 15h²

Step-by-step explanation:

Since both have same function i. e. function of f, so we simply put 6 + h and 6 in place of x in f (x)

Here,

f (x) = 15x² + 6

Then, f (6+h) - f (6)

= [15 (6 + h) ² + 6] - [15 (6) ² + 6]

⇒ [15 (36 + 12h + h²) + 6] - [15 * 36 + 6]

⇒ [ 15 * 36 + 15 * 12h + 15h² + 6 - 15 * 36 - 6 ]

⇒ 15 * 12h + 15h²

⇒ 180h + 15h²