Question #1ba37 Calculus Graphing with the First Derivative Mean Value Theorem for Continuous Functions 1 Answer Jim H Dec 3, 2017 Solve #f'(x) = (f(1)-f(-1))/(1-(-1)# in the interval #(-1,1)#. Explanation: #f'(x) = 24x+8# #(f(1)-f(-1))/(1-(-1)) = (28-12)/(1-(-1))= 14/2 = 7# #24+8 = 7# at #x = -1/24# There is only one value that works for #c#, #c = -1/24# 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 1156 views around the world You can reuse this answer Creative Commons License