Consider function f(x)=2−7x2,−4≤x≤2. The absolute maximum value is and this occurs at x= The absolute minimum value is and this occurs at x=

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Consider function f(x)=2−7x2,−4≤x≤2.  The absolute maximum value is  and this occurs at x=  The absolute minimum value is  and this occurs at x=

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Step 1 : AnalysisGiven :f(x)=2−7x2Step 2 : SimplificationWe have,f(x)=2−7x2We will calculate the derivative of f(x),f′(x)=ddx(2−7x2)f′(x)=ddx(2)−7ddx(x2)f′(x)=0−7×2xf&#039;(x)=-14xThe critical point is where f&#039;(x)=0 or f&#039;(x) is not defined.Equating f&#039;(x) to zero,f&#039;(x)=0-14x=0x=−014x=0Step 3 : Calculating the values at the critical points and endpoints.We will check the values of the function f(x) at the critical point x=0 and endpoints of the interval that is at x=-4 and x=2,At x=-4,f(−4)=2−7(−4)2f(−4)=2−7×16f(-4)=-110At x=2,f(2)=2−7(2)2f(2)=2−7×4f(2)=-26At x=0,f(0)=2−7(0)2f(0)=2−7×0f(0)=2Step 4 : SolutionThe absolute maximum value is 2 and this occurs at x=0.The absolute minimum value is -110 and this occurs at x=-4.

Consider function f(x)=2-7x^{2}, -4\le x\le 2. The absolute maximum value is and

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