Let f(x) be a polynomial of degree four, having extreme value at x = 1 and x = 2.

If  then f(2) is?

Concept:

To find extreme values of a function f , set f'(x)=0 and solve.

Calculation:

Consider a polynomial f(x) = 

Now, let d = e = o

f(x) = 

f'(x) = 

Here, extreme values are 1 and 2, so f'(1) = f'(2) = 0

f'(1) = 4a + 3b + 4= 0 

Multiply above equation by 4, we get 

16a + 12b + 16 = 0 ....(1)

And f'(2) = 32a + 12b + 8 =0 .....(2)

Subtract (1) from (2), we get 

16a - 8 = 0

⇒ a = 1/2

Put a = 1/2 in (1), we get 

8 + 12b + 16 = 0

⇒ b = -2 

f(x) =