Find the largest open interval where the function is changing as requested. -Increasing f(x) = x² - 2x + 1 A) (0, $\infty$) B) (1, $\infty$) C) (-$\infty$, 1) D) (-$\infty$, 0)

Question

Quizplus · Accepted Answer

To determine where the function $f(x) = x^{12} - 2x + 1$ is increasing, we find its derivative and analyze its sign. The derivative is $f'(x) = 12x^{11} - 2$. Setting $f'(x) > 0$ to find where the function is increasing gives $12x^{11} - 2 > 0$, which simplifies to $x^{11} > \frac{1}{6}$. This inequality is satisfied for $x > 1$ and $x < -1$, but since $x^{11}$ grows faster than linearly, the critical point at $x = 1$ is where the function starts increasing continuously to infinity. Thus, the function is increasing on the interval $(1, \infty)$.

Find the Largest Open Interval Where the Function Is Changing ∞\infty∞

Find the Largest Open Interval Where the Function Is Changing $\infty$