Question 91
What is the derivative of $f(x) = x^91$ at x = 1?
Detailed Solution
f'(x) = 91 $x^{90}$. At x = 1, f'(1) = 91.
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Question 92
Consider the function f(x) = (x - $92)^2$. Which of the following statements are TRUE?
Detailed Solution
f(92) = 0, f'(92) = 0, f''(92) = 2 > 0 (so x = 92 is a local MINIMUM, not maximum).
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Question 93
Find the value of $\lim_{x \to 93} \frac{x^2 - 93^2}{x - 93}$.
Detailed Solution
Using L'Hopital's rule or factoring: $(x^2 - 93^2)/(x - 93)$ = x + 93. At x = 93, limit = 186.
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Question 94
What is the derivative of $f(x) = x^94$ at x = 1?
Detailed Solution
f'(x) = 94 $x^{93}$. At x = 1, f'(1) = 94.
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Question 95
Consider the function f(x) = (x - $95)^2$. Which of the following statements are TRUE?
Detailed Solution
f(95) = 0, f'(95) = 0, f''(95) = 2 > 0 (so x = 95 is a local MINIMUM, not maximum).
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