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Rolle's Theorem as a Special Case of LMVT
If:
$$f(a)=f(b)$$
then the LMVT relation:
$$f'(c)=\frac{f(b)-f(a)}{b-a}$$
reduces to:
$$f'(c)=0$$
Usage
- Used to recognize Rolle's theorem as a special case of the Lagrange Mean Value Theorem.
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Rolle's Theorem as a Special Case of LMVT
If:
$$f(a)=f(b)$$
then the LMVT relation:
$$f'(c)=\frac{f(b)-f(a)}{b-a}$$
reduces to:
$$f'(c)=0$$
Usage
- Used to recognize Rolle's theorem as a special case of the Lagrange Mean Value Theorem.
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