Use the derivative to find any critical points of the function. Then find the maximum and minimum points of graph on the given interval.; [-3,3] 相关知识点: 试题来源: 解析 critical points: and ; max: 25, min: -5 反馈 收藏
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the derivative. For example, a derivative that exists everywhere is a function of class one in the Baire classification. A derivative, even if it is discontinuous, takes on all intermediate values between its maximum and minimum. The most important generalizations of the concept of derivative ...
Determine the point at which f(x) is maximum. Sign of Second Derivative: A function's maximum or minimum can be identified by looking at the symbol for the second derivative of that function. If the sign of y″ is positive at the extreme point...
We study the fractional diffusion problem, where time evolution is determined by the scale function-dependent Caputo derivative and show that the maximum or respectively minimum principle is valid, provided the source function is a non-positive or a non-negative one in the domain. As an ...
Another application is finding extreme values of a function, so the (local) minimum or maximum of a function. Since in the minimum the function is at it lowest point, the slope goes from negative to positive. Therefore, the derivative is equal to zero in the minimum and vice versa: it ...
Answer to: Find the local maximum and minimum values of f using both the First and Second Derivative Tests. \\ f(x) = 3 + 9x^2- 6x^3 By signing up,...
WhenΔx<0Δx<0and|Δx||Δx|is small enough,f′(x0+Δx)−f′(x0)<0f′(x0+Δx)−f′(x0)<0,sof′(x0+Δx)<0f′(x0+Δx)<0.Sox0x0is a local minimum(why?According to the differential mean value theorem.) Remark 1:Similarly, ...
We see how to locate its maximum and minimum values and its points of inflection, and we see how to analyze the relationship between average and marginal costs. As we saw in Chapter 2, the derivatives of a function and the function itself are connected in the following way: • If f >...
A derivative, even if it is discontinuous, takes on all intermediate values between its maximum and minimum. The most important generalizations of the concept of derivative follow. Dini derivatives. The superior limit of the ratio as x1→x, x1 > x, is called the right upper derivative of f...