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Question

Consider the function f(x)=x24x+17. If M and m are the maximum and minimum values of f in [0,3] respectively, then the value of 2Mm is

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Solution

f(x)=x24x+17
Here, a=1>0
D=52<0
So, the graph of y=f(x) lies above x-axis.
The graph of y=f(x) looks like


Minimum value occurs at x=b2a=2
m=f(2)=13
Maximum value of f will occur at one of the end points of the interval [0,3]
f(0)=17 and f(3)=14
M=max{f(0),f(3)}=17
Hence, 2Mm=21

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