1wow....y cant i think like that!!!! thanx bhaiya...
Consider the polynomial f(x) = ax2+bx+c.
If f(0) = 0 and f(2) = 2, find the minimum value of \int_{0}^{2}{\left|f'(x) \right|}dx equals??
i get 2a+b=1 (simple), but how to get the value of -b/2a??
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3 Answers
1well one thing that can straight of be said is determinant > 0
so try graphing the quadratic and
answer has to be in terms of a or b
given data is insufficient in my opinion
62f(0)=0 means that c=0
f(2)=2 means that 4a+2b=2 so 2a+b=1
Now f'(x)=2ax+b=2ax+1-2a=2a(x-1)+1
f'(x)=0 at x=1-1/2a
when we are integrating from 0 to 2 we have to break the limits from 0 to 1-1/2a and then from 1-1/2a to 2
and then find the integral...
Can you finish the rest off?