Find the first derivative of f using the power rule.

Set the derivative equal to zero and solve for x.

x = 0, 2, or 2.

These three x-values are the critical numbers of f. Additional critical numbers could exist if the first derivative were undefined at some x-values, but because the derivative

is defined for all input values, the above solution set, 0, 2, and 2, is the complete list of critical numbers. They are found by setting derivative of the cubic equation equal to zero obtaining: f (x) = 3ax2 + 2bx + c = 0. Maxima and Minima from Calculus. How to find local max and min using first derivative test | Math Index Get support from expert teachers If you're looking for expert teachers to help support your learning, look no further than our online tutoring services. PDF Local Extrema - University of Utah Without using calculus is it possible to find provably and exactly the maximum value or the minimum value of a quadratic equation $$ y:=ax^2+bx+c $$ (and also without completing the square)? When working with a function of one variable, the definition of a local extremum involves finding an interval around the critical point such that the function value is either greater than or less than all the other function values in that interval. DXT DXT. To find local maximum or minimum, first, the first derivative of the function needs to be found. Again, at this point the tangent has zero slope.. Based on the various methods we have provided the solved examples, which can help in understanding all concepts in a better way. To find local maximum or minimum, first, the first derivative of the function needs to be found. See if you get the same answer as the calculus approach gives. How do we solve for the specific point if both the partial derivatives are equal? 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. How to find maxima and minima without derivatives Rewrite as . @Karlie Kloss Technically speaking this solution is also not without completion of squares because you are still using the quadratic formula and how do you get that??? So, at 2, you have a hill or a local maximum. ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/8985"}}],"_links":{"self":"https://dummies-api.dummies.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"