Question
Find the biggest value of c that satisfy the Mean Value Theorem for integrals for
f(x)= 1/(x+1)^6 on the interval [0,7]
f(x)= 1/(x+1)^6 on the interval [0,7]
Answers
Steve
the slope of the secant is (1/8^6 - 1)/7 ≈ -1/7
f' = -6/(x+1)^7
so, you want
-6/(c+1)^7 = -1/7
c ≈ 0.7
c is in the interval
Since f is monotonically decreasing, there is no other value for c.
f' = -6/(x+1)^7
so, you want
-6/(c+1)^7 = -1/7
c ≈ 0.7
c is in the interval
Since f is monotonically decreasing, there is no other value for c.