A function f has second derivative f''(x) = (x + 2)x^2(x - 1)^3(x - 4)^4. For which values of x does the function have inflection points? The derivative of a function f is given by f'(x) = x(x - 1)(x + 2)2. Determine the point of inflection. ...
The second derivative may be used to identify the local extrema of a function under different conditions. If a function has a critical point for which f'(x)=0 and the second derivative is positive, then f is minimum at ...
So, we'll compute the second derivative at the critical point and if {eq}f''(x)>0 {/eq} then that point is the local minima, if {eq}f''(x)<0 {/eq} then that point is the local maxima. Answer and Explanation:1 We are given: ...
EitherFind the gradient either side of the stationary pointIf gradient changes from +ve to -ve:maxIf gradient changes from -ve to +ve:minOr Alternative 1Take the second derivative and substitute in the value of x obtained in (b)If second derivative is +ve,then a minIf second derivative ...
Kinetic parameters of glow peaks (as many as 14 in the range of 75–575°C) of colorless microcline have been successfully achieved to a high degree of certainty by resorting to computerized glow curve deconvolution (CGCD) in the framework of kinetics formalism. The second derivative plot of ...
Step 1We'll need the first derivative to get the answer to this problem so let's get that.Step 2Recall that critical points are simply where the derivative is zero and/or doesn't exist.This derivative exists everywhere and so we don't need to worry about that. Therefore, all we need...
Concavity and the Inflection Points:The second derivative can be used to check the concavity and the inflection points of a function. Concavity (concave up or concave down) changes if the sign of the second derivative changes. The inflection...
5.7 Using the Second Derivative Test to Determine Extrema微积分 41 -- 14:31 App 7.2 Verifying Solutions for Differential Equations AP微积分 79 -- 13:52 App 5.11 Solving Optimization Problems AP微积分 54 -- 9:58 App 4.7 L'Hopital's Rule微积分 71 -- 21:36 App 1.3 Finding Limits from...
(ii) Hence· find the coordinates of the stationary point,determine the nature of the stationary point. 相关知识点: 试题来源: 解析 theirsubstitution of theirin their second derivativewhich is positive sois a minimumFT their; dependent on (i)(B) involvingWww ...
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