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  

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