GATE 2021 ST – Question 55
Let f(x,y)=8x²−2y. If M,m are its maximum and minimum on x²+y²=1,find M−m,to two decimals.
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Correct answer: 10.10 to 10.15
Explanation
Substitute x²=1−y² to get f=8−8y²−2y=65/8−8(y+1/8)² for −1≤y≤1. Its maximum is 65/8 at y=−1/8. The concave quadratic reaches its minimum at an endpoint:values are −2 at y=1 and 2 at y=−1. Thus M−m=65/8+2=81/8=10.125,reported **10.13** to two decimals.