I'm studying for a test and I came across this problem in the review and I'm getting a different answer than the answer key
$$f(x) = x^3 - 4x$$
Difference quotient: $\frac{f(1+h)-f(1)}{h}$
I'm getting the answer $h^2 + 3h + 7$ but the answer key says $-1+3h+h^2$
Can anyone tell me what I'm doing wrong? Thank you!
I think you may have made an error with a negative sign.
$f(x) = x^3 - 4x \\ f(1) = 1^3 - 4 \times 1 = -3 \\ f(1+h) = (1+h)^3 - 4(1+h) = (1 + 3h + 3h^2 + h^3) - (4 + 4h) = h^3 + 3h^2 - h - 3 \\ f(1+h) - f(1) = h^3 + 3h^2 - h \\ (f(1+h) - f(1))/h = h^2 + 3h - 1$