Hi guys, I don't know how to do this problem:
Find and simplify
[f(x + h) − f(x)] / h where (h ≠ 0)
for the function.
f(x) = 6x^2 − 4x + 7
Find and simplify
[f(x + h) − f(x)] / h where (h ≠ 0)
for the function.
f(x) = 6x^2 − 4x + 7
-
f(x+h) = 6(x+h)² − 4(x+h) + 7
= 6(x² + 2xh + h²) − 4x − 4h + 7
= 6x² + 12xh + 6h² − 4x − 4h + 7
f(x+h) − f(x) = 6x² + 12xh + 6h² − 4x − 4h + 7 − (6x² − 4x + 7)
= 12xh + 6h² − 4h
= h(12x + 6h − 4)
[f(x+h) − f(x)] / h = h(12x + 6h − 4) / h
For h ≠ 0 we may cancel the common factor of h in the numerator and denominator, leaving us with
[f(x+h) − f(x)] / h = 12x + 6h − 4
= 6(x² + 2xh + h²) − 4x − 4h + 7
= 6x² + 12xh + 6h² − 4x − 4h + 7
f(x+h) − f(x) = 6x² + 12xh + 6h² − 4x − 4h + 7 − (6x² − 4x + 7)
= 12xh + 6h² − 4h
= h(12x + 6h − 4)
[f(x+h) − f(x)] / h = h(12x + 6h − 4) / h
For h ≠ 0 we may cancel the common factor of h in the numerator and denominator, leaving us with
[f(x+h) − f(x)] / h = 12x + 6h − 4