Given function is:

⇒ f(x) = 2x² – 5x + 3 on [1,3]

Since given function ‘f’ is a polynomial. So, it is continuous and differentiable every where.

Now, we find the values of function at the extremum values.

⇒ f(1) = 2(1)²–5(1) + 3

⇒ f(1) = 2 – 5 + 3

⇒ f(1) = 0 ......(1)

⇒ f(3) = 2(3)²–5(3) + 3

⇒ f(3) = 2(9)–15 + 3

⇒ f(3) = 18 – 12

⇒ f(3) = 6 ......(2)

From (1) and (2), we can say that,

f(1)≠f(3)

∴ Rolle’s theorem is not applicable for the function f in interval [1,3].