Question

verify rolle's theorem for the function f(x)=X^2-3x+2, x∈[1,2]

Answer 1

Answer: The function, f(x)=x^2-3x+2, x∈[1,2], satisfies all the conditions of rolle's theorem, so it verifies rolle's theorem.

Step-by-step explanation:

f(x)=x^2-3x+2, is a polynomial function hence this function is continuous on [1,2].

f'(x)= 2x-3, It is clear that f(x) is also differentiable on(1,2).

f(1)= 1^2-3*1+2=0

f(2)= 2^2-3*2+2=0

So,

f(1)=f(2)

Therefore, there exists a number c in (1,2) such that f'(c)=0

2c-3=0

=> c=3/2

Here, c=3/2 belongs to (1,2), it verifies rolle's therem.