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 1191 views around the world You can reuse this answer Creative Commons License