Find and simplify (f(a + h) − f(a))/h , (h ≠ 0) for the function. f(x) = 6x^2 − 6x + 7

Question

Find and simplify (f(a + h) − f(a))/h , (h ≠ 0) for the function. f(x) = 6x^2 − 6x + 7

Answer 1

f(x) = 6x²-6x+7

 

f(a+h) = 6(a+h)²-6(a+h)+7

= 6(a²+2ah+h²) - 6a - 6h + 7

= 6a² + 12ah+6h² - 6a - 6h +7

 

f(a) = 6a²-6a+7

 

f(a+h)-f(a) = 12ah + 6h² - 6h

 

[f(a+h)-f(a)]/h = 12a + 6h - 6