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| # | Question | Subject and topic | Difficulty |
|---|---|---|---|
| 4321 | The radius of a circle increases at 0.5 cm/s. How fast is its area increasing when the radius is 4 cm? | Mathematics/Applied Mathematics Rate of change |
Medium |
| 4322 | Each side of a cube increases at 3 cm/s. At what rate is the volume increasing when a side is 10 cm? | Mathematics/Applied Mathematics Rate of change |
Medium |
| 4323 | Air is pumped into a spherical balloon so that its volume increases at 900 cm³/s. How fast is the radius incr… | Mathematics/Applied Mathematics Rate of change |
Hard |
| 4324 | The function f(x) = 3x + 7 is | Mathematics/Applied Mathematics Increasing and decreasing functions |
Easy |
| 4325 | On which interval is f(x) = x² strictly decreasing? | Mathematics/Applied Mathematics Increasing and decreasing functions |
Easy |
| 4326 | The function f(x) = x³ − 3x is strictly decreasing on | Mathematics/Applied Mathematics Increasing and decreasing functions |
Medium |
| 4327 | The function f(x) = 2x³ − 9x² + 12x + 1 is strictly decreasing on | Mathematics/Applied Mathematics Increasing and decreasing functions |
Medium |
| 4328 | For which values of a is f(x) = x³ + ax + 5 strictly increasing on all of R? | Mathematics/Applied Mathematics Increasing and decreasing functions |
Hard |
| 4329 | The minimum value of x² + 4x + 9 is | Mathematics/Applied Mathematics Maxima and minima |
Easy |
| 4330 | If f′(c) = 0 and f″(c) > 0, then at x = c the function f has | Mathematics/Applied Mathematics Maxima and minima |
Easy |
| 4331 | The local maximum value of f(x) = x³ − 3x is | Mathematics/Applied Mathematics Maxima and minima |
Medium |
| 4332 | Two positive numbers have a sum of 20. What is the largest possible value of their product? | Mathematics/Applied Mathematics Maxima and minima |
Medium |
| 4333 | The absolute maximum value of f(x) = 2x³ − 15x² + 36x + 1 on the interval [1, 5] is | Mathematics/Applied Mathematics Maxima and minima |
Hard |
| 4334 | ∫ x⁴ dx equals | Mathematics/Applied Mathematics Indefinite integrals |
Easy |
| 4335 | ∫ sec²x dx equals | Mathematics/Applied Mathematics Indefinite integrals |
Easy |
| 4336 | ∫ (2x + 3/x) dx equals | Mathematics/Applied Mathematics Indefinite integrals |
Medium |
| 4337 | ∫ e^(2x) dx equals | Mathematics/Applied Mathematics Indefinite integrals |
Medium |
| 4338 | If F′(x) = 3x² + 2x and F(1) = 5, then F(x) equals | Mathematics/Applied Mathematics Indefinite integrals |
Hard |
| 4339 | To evaluate ∫ 2x cos(x²) dx, the most useful substitution is | Mathematics/Applied Mathematics Methods of integration |
Easy |
| 4340 | ∫ x eˣ dx equals | Mathematics/Applied Mathematics Methods of integration |
Easy |