For f(x)=3x2−4x+2, find the absolute maximum and minimum on [-2,2] using Calculus

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For f(x)=3x2−4x+2,  find the absolute maximum and minimum on [-2,2] using Calculus

Julie Mathew · Accepted Answer

Step 1  The points of local minimum and local maximum can be obtained by differentiating the function and equating it to 0. The range of values of the variable for which the second derivative is positive is the range where the function is concave up. The range of values of the variable for which the second derivative is negative is the range where the function is concave down.   Step 2  The function is differentiated and equated to 0 as follows:-  df(x)dx=0  ddx(3x2−4x+2)=0  6x-4=0  x=23  The values of the function at x=23 and at the boundary points x=-2 and x=2 are calculated as follows:-  f(x)=3x2−4x+2  f(23)=3(23)2−4⋅23+2  =23  f(−2)=3(−2)2−4(−2)+2  =22  f(2)=3⋅22−4⋅2+2  =6  The absolute minimum value of the function is obtained as 23. The absolute maximum value of the function is obtained as 22.

For f(x)=3x^{2}-4x+2, find the absolute maximum and minimum on [-2,2] using

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