Mathematics I20775 marksNumerical: Rolle's theorem verificationMean value theorem
State Rolle's theorem and verify the Rolle's theorem for f(x) = x3 - x2 - 6x + 2 in [0, 3].
State Rolle's theorem and verify the Rolle's theorem for $f(x) = x^3 - x^2 - 6x + 2$ in [0, 3]. [5]
- Function: $f(x) = x^3 - x^2 - 6x + 2$ - Interval: $[0, 3]$, so $a = 0$, $b = 3$ If a function $f$ satisfies: 1. $f$ is continuous on the closed interval $[a, b]$ 2. $f$ is differentiable on the open interval $(a, b)$ 3. $f(a) = f(b)$ then there exists at least one point $c \in (a, b)$ such that...