State Rolle's theorem and verify the theorem for f(x) = x2 - 9, x in [ | Mathematics I 2079

Mathematics I20795 marksNumerical: Rolle's theorem verificationMean value theorem

State Rolle's theorem and verify the theorem for $f(x) = x^2 - 9$ , $x \in [-3,3]$ . [5]

State Rolle's theorem and verify the theorem for $f(x) = x^2 - 9$, $x \in [-3,3]$. [5]

Function: $f(x) = x^2 - 9$ - Interval: $[a, b] = [-3, 3]$ --- 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 $f'(c) = 0.$ ...

Function: $f(x) = x^2 - 9$ - Interval: $[a, b] = [-3, 3]$ --- 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 $$f'(c) = 0.$$...

State Rolle's theorem and verify the theorem for f(x) = x2 - 9, x in [-3,3].