Question

Verify whether the function f(x) = x2 -4x + 3 on the interval (1, 3) satisfies the conditions of Rolle's Theorem and then find all values of x = c such that f'(c )= 0.

Answer 1

Som we have to verify whether the function of(x) = x2-41 +3 on interval [13] Satisfies the condition of Rulle's theorem or not $ them find the value of x=c such that f'(c) = 0 Since, f(x) = 42-4x+3 60137 1 (1) n is +2) from equation (i), we say that since f(x) = x²-4x+3 is Polynomial of Degree 2 & As we know that every polynomial of degree continous & differentiable on any intercal. soru, F(x) = x2-48+3 is continous in occ [13] Also from = 24-4x+3 is differentiable in 26(13] ci so, frous = 82-49€+3 is differentiable in ICG (13) & fiy 124+3 = -32-4*3+3 that f(1) = 0 =f(3). then from equation (2), (3) and (4), we say that satisfied F(x)=x2-4x+3 , XE [13] the condition of Rollie's theorem. there exist CE(13). such that F'CCI 20 +3) f(3) = -9-12 +370 Hence, 20-4 2= 2