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Mean Value Theorem for Derivative Bounds
If:
$$m\leq f'(x)\leq M$$
for every $$x\in[a,b]$$, then:
$$m(b-a)\leq f(b)-f(a)\leq M(b-a)$$
Usage
- Used to establish bounds on function values from bounds on its derivative.
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Mean Value Theorem for Derivative Bounds
If:
$$m\leq f'(x)\leq M$$
for every $$x\in[a,b]$$, then:
$$m(b-a)\leq f(b)-f(a)\leq M(b-a)$$
Usage
- Used to establish bounds on function values from bounds on its derivative.
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