Consider the function f(x)=3−4x2,−4≤x≤1. 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 the function f(x)=3−4x2,−4≤x≤1.  The absolute maximum value is  and this occurs at x=  The absolute minimum value is  and this occurs at x=

Andrew Reyes · Accepted Answer

Step 1Given thatf(x)=3−4x2,−4≤x≤1Here endpoints of interval are -4 and 1Step 2Differentiate the function with respect to xf′(x)=ddx[f(x)]=ddx(3−4x2)=0-4(2x)=-8xStep 3Equate f′(x) to zero and find the critical point.f&#039;(x)=0-8x=0x=0Step 4Absolute maximum and minimum occur at the critical point or at the endpoints.Find the value of f(x) at the endpoints (x = -4, 1) and at the critical point (x = 0)At x=-4, f(−4)=3−4(−4)2=−61At x=0, f(0)=3−4(0)2=3At x=1, f(1)=3−4(1)2=−1Step 5Function is maximum at x = 0. So, absolute maximum value is 3 and this occurs at x = 0.Function is minimum at x = -4. So, absolute minimum value is -61 and this occurs at x = -4.

Consider the function f(x)=3-4x^{2}, -4\le x\le 1. The absolute maximum value

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