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 1292 views around the world You can reuse this answer Creative Commons License