Question

-) Verify Mean Value Theorem for the function f(x)= x2 - 4x-3, xe[1,4]​

Answer 1

Answer:

Step-by-step explanation: given,

f(X)=x^2-4x-3

f(1)=1-4-3= -6 and,

f(4)=16-16-3= -3

and we for LMVT,

f'(c)=[f(4)-f(1)]/(4-1)

= {-3-(-6)}/3

= 1 .... (1)

NOW, From given function,

f'(x)= 2x-4 ...(2)

Equation (1)and(2) must be equal

i,e. 2x-4=1

2x=5

x= 5/2 which £[1,4] which proves LMVT.