Considering the given function, we have that:
- f(a + h) = 6a² + 12ah + 6h² - 2a - 2h + 4.
- [f(a + h) - f(a)]/h = 12a + 6h - 2.
What is the function for this problem?
The function is:
f(x) = 4 - 2x + 6x².
When x = a, we have that:
f(a) = 4 - 2a + 6a².
When x = a + h, we have that:
f(a + h) = 4 - 2(a + h) + 6(a + h)² = 6a² + 12ah + 6h² - 2a - 2h + 4.
For the fraction, we have that:
[f(a + h) - f(a)]/h = [6a² + 12ah + 6h² - 2a - 2h + 4 - 4 + 2a - 6a²]/h = [12ah + 6h² - 2h]/h = h(12a + 6h - 2)/h
Hence:
[f(a + h) - f(a)]/h = 12a + 6h - 2.
More can be learned about functions at https://brainly.com/question/25537936
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