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Uniqueness of a Root Using Derivative
If:
$$f(a)f(b)<0$$
and:
$$f'(x)>0$$
throughout $$[a,b]$$, then $$f(x)=0$$ has exactly one root in $$[a,b]$$.
Usage
- Used to prove both existence and uniqueness of a root.
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Uniqueness of a Root Using Derivative
If:
$$f(a)f(b)<0$$
and:
$$f'(x)>0$$
throughout $$[a,b]$$, then $$f(x)=0$$ has exactly one root in $$[a,b]$$.
Usage
- Used to prove both existence and uniqueness of a root.
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