How do you determine all values of c that satisfy the mean value theorem on the interval [1, 1.5] for #f(x)=sinx#? Calculus Graphing with the First Derivative Mean Value Theorem for Continuous Functions 1 Answer Bdub Apr 6, 2016 #c~~1.25# Explanation: #f'(x)=cosx# Mean Value Theorem #f'(c)=(f(b)-f(a))/(b-a)# #cos c=(f(1.5)-f(1))/(1.5-1)# #cos c=(sin(1.5)-sin(1))/(1.5-1)# #cos c=(sin(1.5)-sin(1))/(1.5-1)# #cos c =0.3120480036# #c=cos^-1 0.3120480036# #c~~1.25# 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 3314 views around the world You can reuse this answer Creative Commons License