Find: Use first derivative to find local max and min values of f (x) = \frac{(\ln x)}{x^\frac{1}{2 Find the local maxima and minima and the range of f(x) = \frac{e^x}{4x^2 + 3}. Find all local extrema of the fu
Soforanon-degeneratecriticalpoint,ifitsMI=0,thenitisalocalminimizerandastable solution,andifitsMI>0,thenitisamin-maxtypeand unstable solution. Multiple solutions with different performance and instability exist in many nonlinear problems in natural and social sciences [20, 18, 14, 22, 13]. Stabil...
The inflection point occurs at x = p3. You can show it by using the symbolic 'diff' to find the second derivative of f with respect to x and finding the x that makes it zero. That occurs when 10^((p3-x)*p4)) is equal to 1 which forces x to equal p3. ...
On each piece it has no local maxima and possibly one local minimum interior to the interval. By splitting intervals at such minima, the distance function is a piece-wise monotone function. We will therefore solve the following more general version of the problem: Given a piece-wise monotone ...
Such a theorem comes from directional derivative considerations of a convex functional and is discussed in design monographs like (Fedorov 1972; Berger and Wong 2005). For example, if m is the dimension of θ and δx is the design that takes all observations at x, it can be shown that ...
This allows us to state the optimality of using the channel for which the derivative of losses in stream has the smallest value. This conclusion is of great importance and will be used further in this study. At the same time, finding the value of the function 𝐿𝑜𝑠𝑠(𝑥)Loss(x...
which is a derivative of nerolidol. The terpene synthase enzyme nerolidol synthase (NES) was previously reported in lima beans (Phaseolus lunatusL.), maize (Zea maysL.), and cucumber (Cucumis sativusL.), and was shown to catalyze the biosynthesis of the DMNT precursor nerolidol from farnesyl ...