How will this be done?
A monic polynomial function of degree 5 increases in the interval and and decreases in the interval . Call the polynomial obtained by differentiating once with respect to .
Given that and . Calculate the value of .
If you think that the data is insufficient, then submit 1 as your answer.
The answer is 60.
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1 solution
It's given that p(x) increases for x<1, and for x>3 and it decreases for 1<x<3. So f(x) is positive before x =1 and negative after 1. As f(x) is continuous, f(1) is 0. Similarly f(3)=0. Now we know that f(2) is also 0. But we know that f(x) is non positive for (1,3) so we can say that f(x) touches the X axis at 2. Now as f (x) is 4 degree polynomial with leading coefficient 5, and has factors x-1 and x-3 and (x-2)² we get f(x) as 5(x-1)(x-2)²(x-3).