Question #4f1cd Calculus Graphing with the First Derivative Mean Value Theorem for Continuous Functions 1 Answer Jim H Sep 9, 2016 I assume this is #f(x) = x^2+1#, in which case the number you want is #1/2#. Explanation: The #c# in the conclusion of MVT is every number in #(0,1)# that satifies #f'(x) = (f(1)-f(0))/(1-0)#. Solving #2x = (2 - 1)/(1-0)#, we fet #x = 1/2#. Answer link Related questions What is the Mean Value Theorem for continuous functions? What is Rolle's Theorem for continuous functions? How do I find the numbers #c# that satisfy the Mean Value Theorem for #f(x)=3x^2+2x+5# on the... How do I find the numbers #c# that satisfy the Mean Value Theorem for #f(x)=x^3+x-1# on the... How do I find the numbers #c# that satisfy the Mean Value Theorem for #f(x)=e^(-2x)# on the... How do I find the numbers #c# that satisfy the Mean Value Theorem for #f(x)=x/(x+2)# on the... How do I use the Mean Value Theorem to so #4x^5+x^3+2x+1=0# has exactly one real root? How do I use the Mean Value Theorem to so #2x-1-sin(x)=0# has exactly one real root? How do I find the numbers #c# that satisfy Rolle's Theorem for #f(x)=sqrt(x)-x/3# on the... How do I find the numbers #c# that satisfy Rolle's Theorem for #f(x)=cos(2x)# on the interval... See all questions in Mean Value Theorem for Continuous Functions Impact of this question 1201 views around the world You can reuse this answer Creative Commons License