Suppose that f is continuous on the interval [0,1], that f(0)=2, and that f has no zeros in the

Name: Suppose that f is continuous on the interval [0,1], that f(0)=2, and that f has no zeros in the interval. Prove that f(x)>0 for all x in [0,1].
Uploaded: 2022-02-16T17:12:26-08:00
Duration: 2 min 29 s
Channel: Ma. Theresa Alin
Description: Suppose that f is continuous on the interval [0,1], that f(0)=2, and that f has no zeros in the interval. Prove that f(x)>0 for all x in [0,1].

Question

Ma. Theresa Alin · Accepted Answer

Step 1: Assume by contradiction that there exists a point $c$ in the interval $[0,1]$ such that

Question

Suppose that $f$ is continuous on the interval $[0,1],$ that $f(0)=2,$ and that $f$ has no zeros in the interval. Prove that $f(x)>0$ for all $x$ in [0,1].

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