Question

let f(x) = 2x^2+5-e^x , use the intermediate value theorem to show that the f(x) has a root in the interval [3,4]?

Answer 1

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Answer:

sign(f(3)) ≠ sign(f(4))

Explanation:

The intermediate value theorem tells you that a sign change between f(a) and f(b) means there is a root in the interval [a, b].

Here, we have f(3) ≈ +2.9 and f(4) ≈ -17.6, so there is a root in [3, 4].

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The root is approximately 3.27560108885.