Consider the function f(x) = (x - $71)^2$. Which of the following statements are TRUE?
f(71) = 0, f'(71) = 0, f''(71) = 2 > 0 (so x = 71 is a local MINIMUM, not maximum).
Find the value of $\lim_{x \to 72} \frac{x^2 - 72^2}{x - 72}$.
Using L'Hopital's rule or factoring: $(x^2 - 72^2)/(x - 72)$ = x + 72. At x = 72, limit = 144.
What is the derivative of $f(x) = x^73$ at x = 1?
f'(x) = 73 $x^{72}$. At x = 1, f'(1) = 73.
Consider the function f(x) = (x - $74)^2$. Which of the following statements are TRUE?
f(74) = 0, f'(74) = 0, f''(74) = 2 > 0 (so x = 74 is a local MINIMUM, not maximum).
Find the value of $\lim_{x \to 75} \frac{x^2 - 75^2}{x - 75}$.
Using L'Hopital's rule or factoring: $(x^2 - 75^2)/(x - 75)$ = x + 75. At x = 75, limit = 150.
