f'(t)=e^t(3-t)+e^t*(-1)=e^t*(2-t)令f'(t)=0,即e^t*(2-t)=0因e^t>0,则2-t=0即t=2显然当t<2时f'(t)>0,说明函数为增函数所以在区间[-1.2,1]上f(t)为增函数于是有f(t)max=f(1)=2e,f(t)min=f(-1.2)=(9/5)e^(-6/5) 反馈 收藏 ...
4.1ExtremeValuesof Functions DefinitionAbsoluteExtremeValues LetfbeafunctionwithdomainD.Thenf(c)isthe a.absoluteminimumvalueonDifandonly iff(x) b.absolutemaximumvalueonDifandonly iff(x)>f(c)forallxinD. Extremevaluescanbeintheinteriorortheend
Linearity of Differentiation Linearly Independent Solutions Logarithm M MacLaurin Series Many to One Mean Value Theorem Min-Max Theorem Moment Monotonic Sequence, Series, Function Multiplicative Calculus Multivariate N Newton Notation Non empty set Nonstandard Calculus Non-Newtonian Calculus n-tuple Numerical...
Increased the number of problems in section 1.7 (Introduction to Limits and Continuity). Augmented the graphical treatment of max/min problems in chapter 4 (Using the Derivative). Added Simpson's rule to more problems in section 7.5 (Numerical Methods for Definite Intervals). ...
We also introduce a new approach to the computation of the derivative of the fuzzy max and min functions using the concept of a generalized function. During the construction of the classifier, based on FRC, we use fuzzy linguistic statements (or fuzzy membership function to represent the ...
Applications of the derivative to "max/min" problems, differential equations, related rates, implicit differentiation, sum/product/chain rules, rates of change, and parametric equations are then studied. Introduction to Integral Calculus STEM Calculus I studies the connection between integrals as ...
Putting Derivatives to Work 04 P7 - 04:29Local Min/Max At a critical point, example: local maximum at x=0, b/c the coefficient of x^4 <0 still, we use 2nd derivative test and Taylor expansion. Example: find global maximum/minimum,check the endpoint. ...
Integration by Parts| ln(x) |n*e^x|sin(x)| cos(x) | sin(x) and cos(x) Intervals of Increase or Decrease Limits| Instructions | Definition | Execute Limit ln(x)| Derivatives ln(x)| Integrals Local Max & Min| Extrema log(x) Log to Other Base| Evaluate | Solve for x | Exponen...
1.4 Graphing Calculators and Computers 1. A graphing calculator or computer displays a rectangular portion of the graph of a function in a display window or viewing screen. If we choose the x-values to range from a minimum 3 1.5. EXPONENTIAL FUNCTIONS value of Xmin a to a maximum value...
Integrate[f,x] the indefinite integral ∫f dx Integrate[f,x,y] the multiple integral ∫dx dy f Integrate[f,{x,xmin,xmax}] the definite integral f dx Integrate[f,{x,xmin,xmax},{y,ymin,ymax}] the multiple integral dxdy fIntegration. Here is the definite integral : In[9]:= ...