Consider the function f(x)=x4−50x2+2,−4≤x≤11. This function has an absolute minimum value equal to what? and an absolute maximum value equal to what?

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Consider the function f(x)=x4−50x2+2,−4≤x≤11. This function has an absolute minimum value equal to what?  and an absolute maximum value equal to what?

Dabanka4v · Accepted Answer

Step 1: Formuladdxxn=n(x)n−1Step 2:Finding the derivativeUsing the formula mentioned in the last step, one need to find the derivative of the given function. f′(x)=4(x)4−1−50(2)(x)2−1+0=4x3−100xStep 3:Finding the critical numbersTo find the critical number, one have to set the derivative of the function to 0 and solve for x4x3−100x=04x(x2−25)=04x=0,x2−25=0x=0,x2=25x=0, x=-5, x=5In the given interval, 0 and 5 lies. So one have to ignore -5Step 4: Finding the value of the function at the boundary and critical valuesBoundary values are -4 and 11Critical numbers are 0 and 5f(−4)=(−4)4−50(−4)2+2=256−800+2=−542f(0)=04−50(0)2+2=2f(5)=54−50(5)2+2=−623f(11)=114−50(11)2+2=8593Step 5:FInding absolute maximum and absolute minimumSince the minimum value is -623, so absolute minimum is -623And since the maximum value is 8593, so the absolute maximum is 8593.

Consider the function f(x)=x^{4}-50x^{2}+2,-4\le x\le 11. This function has an

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