🎓 Academic PATULONG PO

[Budak69]

1. Let 𝑓(𝑥)= 𝑥2. Determine whether or not 𝑓 satisfies the hypothesis of the Mean Value Theorem on the interval [1,2]. If it does, find a number 𝑐 ∈ [1,2] which satisfies the conclusion of the theorem.

2. Let 𝑓 be a polynomial function, and let 𝑎 and 𝑏 be two consecutive roots of the equation 𝑓′(𝑥)=0. Show that 𝑓 has at most one root in the interval [𝑎,𝑏].

3. Use Taylor’s formula to find an estimate for 𝑒−1 which is accurate to five decimal places.


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