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Questions and Answers
At which point does the function $f(x) = x^3 - 3x^2 - 9x + 5$ have a local maximum?
At which point does the function $f(x) = x^3 - 3x^2 - 9x + 5$ have a local maximum?
- $x = -1$
- $x = 3$
- $x = 2$ (correct)
- $x = 0$
What is the derivative of $f(x) = x^3 + 4x^2 + 7x - 2$?
What is the derivative of $f(x) = x^3 + 4x^2 + 7x - 2$?
- $f'(x) = 3x^2 + 4x$
- $f'(x) = 3x^2 + 4x + 7$
- $f'(x) = 3x^2 + 8x + 7$ (correct)
- $f'(x) = 3x^2 + 8x$
What is the limit of $f(x) = \frac{x^2 - 4}{x - 2}$ as $x$ approaches 2?
What is the limit of $f(x) = \frac{x^2 - 4}{x - 2}$ as $x$ approaches 2?
- $f(2) = -\infty$
- $f(2) = 0$
- $f(2) = 1$ (correct)
- $f(2)$ does not exist
For which value of $k$ does the function $f(x) = kx^2 - 4x - 3$ have no critical points?
For which value of $k$ does the function $f(x) = kx^2 - 4x - 3$ have no critical points?
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