In order to ascertain where a function is increasing or decreasing, one should first locate its derivative. A positive derivative indicates that the function is on an upward trend, while a negative derivative signals a downward trend. Places where the derivative is either zero or undefined are referred to as critical points, and these are considered potential areas where the function could switch from an increasing to a decreasing trend, or the other way round.
| Topic | Problem | Solution |
|---|---|---|
| None | Part 2 of 5 For the following function, a) give t… | Find the derivative of the function \(h(x)=3x^3-9x\). |
| None | Sketch the graph of the following function. Indic… | Given the function \(f(x) = -\frac{1}{x-7}\) |
| None | 3.3 Enhanced Homework Part 1 of 10 Points: 0 of 1… | The function given is \(f(x)=\frac{-3}{x-7}\). |
| None | K The graph of a derivative $\mathrm{f}^{\prime}$… | The function $f$ is increasing on intervals where $f'$ is positive and decreasing on intervals wher… |
| None | Where is the function $f(x)=x^{2}+6 x+9$ increasi… | The function \(f(x)=x^{2}+6 x+9\) is a quadratic function. The graph of a quadratic function is a p… |
| None | Graphs of the velocity functions of two particles… | Given the velocity function of a particle, we need to find when the particle is speeding up or slow… |
| None | Use the graph to determine a. open intervals on w… | This question is asking for the intervals where a function is increasing, decreasing, or constant. … |
| None | Find the open intervals where $f(z)=z^{3}+6 z^{2}… | Find the first derivative: \(f'(z) = 3z^2 + 12z + 1\) |