Identifying the critical points of a function is a procedure that involves determining where the derivative of the function is either zero or undefined. These points are of significant importance as they commonly represent local peaks or troughs, or even points of inflection on the function's graph. The process of discovering these critical points necessitates differentiating the function, equating it to zero, and then resolving for x.
| Topic | Problem | Solution |
|---|---|---|
| None | Determine all critical points for the following f… | Given the function \(f(x)=x^{2}-256 \sqrt{x}\), we need to find all the critical points. |
| None | Find the critical point of the function. Then use… | First, we find the critical points of the function by setting the first derivatives equal to zero. … |
| None | Consider the function $f(x)=4 x+4 x^{-1}$. For th… | Given the function \(f(x)=4x+\frac{4}{x}\), we need to find the critical numbers and the value of x… |
| None | The function $f(x)=2 x^{3}-36 x^{2}+210 x-10$ has… | The function given is \(f(x)=2 x^{3}-36 x^{2}+210 x-10\). |
| None | (12) A particle is moving in a straight line. Its… | First, we find the velocity function by taking the derivative of the position function with respect… |