Find the value of $\lim_{x \to 66} \frac{x^2 - 66^2}{x - 66}$.
Using L'Hopital's rule or factoring: $(x^2 - 66^2)/(x - 66)$ = x + 66. At x = 66, limit = 132.
What is the derivative of $f(x) = x^67$ at x = 1?
f'(x) = 67 $x^{66}$. At x = 1, f'(1) = 67.
Consider the function f(x) = (x - $68)^2$. Which of the following statements are TRUE?
f(68) = 0, f'(68) = 0, f''(68) = 2 > 0 (so x = 68 is a local MINIMUM, not maximum).
Find the value of $\lim_{x \to 69} \frac{x^2 - 69^2}{x - 69}$.
Using L'Hopital's rule or factoring: $(x^2 - 69^2)/(x - 69)$ = x + 69. At x = 69, limit = 138.
What is the derivative of $f(x) = x^70$ at x = 1?
f'(x) = 70 $x^{69}$. At x = 1, f'(1) = 70.
