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B ead 2a.y then... rove thut iF P is differentiable on Ca, b) and there is...

B ead 2a.y then... rove thut iF P is differentiable on Ca, b) and there is a constant m Such hat P()m for ai xela,b)then the29.4 Corollary. Let f be a differentiable function on (a, b) such that f(z) = 0 for all Proof If f is not constant on (a, b)

B ead 2a.y then... rove thut iF P is differentiable on Ca, b) and there is a constant m Such hat P'()m for ai xela,b)then there exists a censtant c Such that
29.4 Corollary. Let f be a differentiable function on (a, b) such that f'(z) = 0 for all Proof If f is not constant on (a, b), then there exist r1,2 such that a < 1<r2 <b and f(xi) ^ f(r2). By the Mean Value Theorem, for some x є (x1,x2) we have f'(x) = f(n)-f(zi)メ0, a contradiction
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G (at b all u thore exist a cemstant c Suehn tha

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