Consider the function f(x) = (x - $86)^2$. Which of the following statements are TRUE?
f(86) = 0, f'(86) = 0, f''(86) = 2 > 0 (so x = 86 is a local MINIMUM, not maximum).
Find the value of $\lim_{x \to 87} \frac{x^2 - 87^2}{x - 87}$.
Using L'Hopital's rule or factoring: $(x^2 - 87^2)/(x - 87)$ = x + 87. At x = 87, limit = 174.
What is the derivative of $f(x) = x^88$ at x = 1?
f'(x) = 88 $x^{87}$. At x = 1, f'(1) = 88.
Consider the function f(x) = (x - $89)^2$. Which of the following statements are TRUE?
f(89) = 0, f'(89) = 0, f''(89) = 2 > 0 (so x = 89 is a local MINIMUM, not maximum).
Find the value of $\lim_{x \to 90} \frac{x^2 - 90^2}{x - 90}$.
Using L'Hopital's rule or factoring: $(x^2 - 90^2)/(x - 90)$ = x + 90. At x = 90, limit = 180.
