Find the difference quotient and simplify your answer.
f(x) = x2 − 2x + 3, f(8 + h) − f(8)/H
just plug and chug
f(8+h)-f(8) = (8+h)^2 - 2(8+h) + 3 - (8^2-2*8+3) = h^2 + 14h
so the quotient is just h+14
Thanks sooo much ur the best :))
To find the difference quotient, we first need to evaluate f(8 + h) and f(8).
Given that f(x) = x^2 - 2x + 3, we can substitute 8 + h for x to find f(8 + h):
f(8 + h) = (8 + h)^2 - 2(8 + h) + 3
= (64 + 16h + h^2) - 16 - 2h + 3
= h^2 + 14h + 51
Next, substitute 8 for x to find f(8):
f(8) = 8^2 - 2(8) + 3
= 64 - 16 + 3
= 51
Now, substitute these values into the difference quotient formula and simplify:
(f(8 + h) - f(8)) / h = (h^2 + 14h + 51 - 51) / h
= (h^2 + 14h) / h
= h(h + 14) / h
= h + 14
Therefore, the difference quotient is h + 14.
To find the difference quotient for the function f(x) = x^2 - 2x + 3, we need to express f(x + h) - f(x) / h, where h represents the change in x.
First, let's find f(x + h):
f(x + h) = (x + h)^2 - 2(x + h) + 3
= x^2 + 2hx + h^2 - 2x - 2h + 3
Next, we can substitute f(x + h) and f(x) into the difference quotient formula:
[f(x + h) - f(x)] / h = [(x^2 + 2hx + h^2 - 2x - 2h + 3) - (x^2 - 2x + 3)] / h
Simplifying the numerator:
= (x^2 + 2hx + h^2 - 2x - 2h + 3 - x^2 + 2x - 3) / h
= (2hx + h^2 - 2h) / h
Factoring out an h from the numerator:
= h(2x + h - 2) / h
Canceling out the h terms:
= 2x + h - 2
Finally, simplifying the expression gives us the difference quotient for f(x):
2x + h - 2