Let f (x) = 6-1x+15x^2. Calculate the following values:

f (a) =

f (a+h) =

f (a+h) - f (a) h = for h≠0

Step-by-step explanation:

To find f (a), replace x with a: f (a) = 6-1a+15a^2

To find f (a+h), replace x with (a+h) : f (a+h) = 6 - (a + h) + 15 (a+h) ^2

To find f (a+h) - f (a), expand f (a+h) as given above, and then subtract f (a):

f (a+h) - f (a) = 6 - a - h + 15 (a^2 + 2ah + h^2) - [6 - a + 15a^2]

6 - a - h + 15a^2 + 30ah + 15h^2 - [6 - a + 15a^2]

This simplifies to: f (a+h) - f (a) = - h + 30ah + 15h^2