Find the difference quotient and simplify
f(x)=-7x^2-8x+6
To find the difference quotient, we use the formula:
(f(x + h) - f(x)) / h
Given that f(x) = -7x^2 - 8x + 6, we first need to find f(x + h):
f(x + h) = -7(x + h)^2 - 8(x + h) + 6
= -7(x^2 + 2hx + h^2) - 8x - 8h + 6
= -7x^2 - 14hx - 7h^2 - 8x - 8h + 6
Now we can calculate the difference quotient:
(f(x + h) - f(x)) / h
= (-7x^2 - 14hx - 7h^2 - 8x - 8h + 6 - (-7x^2 - 8x + 6)) / h
= (-7x^2 - 14hx - 7h^2 - 8x - 8h + 6 + 7x^2 + 8x - 6) / h
= (-14hx - 7h^2 - 8h) / h
= -14x - 7h - 8
So, the difference quotient for f(x) = -7x^2 - 8x + 6 is -14x - 7h - 8.