Verify Rolle's theorem for each of the following functions on the indicated intervals(i) f(x) = x2 − 8x + 12 on [2, 6](ii) f(x) = x2 − 4x + 3 on [1, 3](iii) f(x) = (x − 1) (x − 2)2 on [1, 2](iv) f(x) = x(x − 1)2 on [0, 1](v) f(x) = (x2 − 1) (x − 2) on [−1, 2](vi) f(x) = x(x − 4)2 on the interval [0, 4](vii) f(x) = x(x −2)2 on the interval [0, 2](viii) f(x) = x2 + 5x + 6 on the interval [−3, −2]

Verify Rolle's theorem for each of the following functions on the indi

1.	Verify Rolle's theorem for each of the following functions on the indicated intervals(i) f(x) = x2 − 8x + 12 on [2, 6](ii) f(x) = x2 − 4x + 3 on [1, 3](iii) f(x) = (x − 1) (x − 2)2 on [1, 2](iv) f(x) = x(x − 1)2 on [0, 1](v) f(x) = (x2 − 1) (x − 2) on [−1, 2](vi) f(x) = x(x − 4)2 on the interval [0, 4](vii) f(x) = x(x −2)2 on the interval [0, 2](viii) f(x) = x2 + 5x + 6 on the interval [−3, −2]
Answer» Verify Rolle's theorem for each of the following functions on the indicated intervals (i) f(x) = x² − 8x + 12 on [2, 6] (ii) f(x) = x² − 4x + 3 on [1, 3] (iii) f(x) = (x − 1) (x − 2)² on [1, 2] (iv) f(x) = x(x − 1)² on [0, 1] (v) f(x) = (x² − 1) (x − 2) on [−1, 2] (vi) f(x) = x(x − 4)² on the interval [0, 4] (vii) f(x) = x(x −2)² on the interval [0, 2] (viii) f(x) = x² + 5x + 6 on the interval [−3, −2]