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

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