how to find local max and min without derivatives

Obtain the function values (in other words, the heights) of these two local extrema by plugging the x-values into the original function.

Thus, the local max is located at (2, 64), and the local min is at (2, 64). A point x x is a local maximum or minimum of a function if it is the absolute maximum or minimum value of a function in the interval (x - c, \, x + c) (x c, x+c) for some sufficiently small value c c. Many local extrema may be found when identifying the absolute maximum or minimum of a function. we may observe enough appearance of symmetry to suppose that it might be true in general. A maximum is a high point and a minimum is a low point: In a smoothly changing function a maximum or minimum is always where the function flattens out (except for a saddle point). If $a$ is positive, $at^2$ is positive, hence $y > c - \dfrac{b^2}{4a} = y_0$ The only point that will make both of these derivatives zero at the same time is \(\left( {0,0} \right)\) and so \(\left( {0,0} \right)\) is a critical point for the function. Calculate the gradient of and set each component to 0. Do my homework for me. Remember that $a$ must be negative in order for there to be a maximum. \end{align} \begin{align} In other words . wolog $a = 1$ and $c = 0$. ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/8985"}}],"_links":{"self":"https://dummies-api.dummies.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"