Question

Find the value of c that satisfies the Mean Value Theorem for f(x)=√x on the interval [1,4].

Answer 1

c=9/4

D

Explanation:

f(x)=√x

it exists in [1,4]

`f'(x)=(1)/(2)√(x) } \\it ~exists~in~(1,4)\\`

it satisfies both the conditions of Mean Value Theorem.

`f'(c)=(f(4)-f(1))/(4-1) \\(1)/(2√(c) ) =(√(4) -√(1) )/(4-1) \\(1)/(2√(c) ) =(2-1)/(3) \\\\(2√(c))/(1) =(3)/(1) \\squaring\\4c=9\\c=(9)/(4) =2.25 \in(1,4)`