Question

fox) = 5x²+2 on [1,4]

find the value of c that satisfies the hypothesis of mean value theorem

Answer 1

The mean value theorem & let f be a function that satisfies the folloveing hypotheses! 17 I in continuous on the closed interval [a,b]. 2 f is differentiable on the open interval Carb) Then there i n a member ein Carb) Tuch thart fr(e) = f(b) f(a) 6-a. then is f is continu Here the given function fea) = 5x2 + 2 on [q] int is continuous on the closed interval 27 f is differentiable on the open intenrad (14)" then there is a memben e in Coral such that fi(e) = f (4) - f (1) fpca)= 107 Or, noc = Ok, soc - o e = 82 - 7 75 20

- 25 C (1,4). Therefore valve of a= 2.5 that satisfies. the hypothesis of mean value theo sein.