Let f(x) 2x 2 5 e x i) Use the Intermediate Value Theorem to show that f(x) has a root in the interval 3,4 ii) Starting at x 0 3 5 , use the Newton's Method to find the root of the given equation, accurate to six decimal places, that lies in the given interval

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Question: Let f(x)=2x^2 + 5 - e^x i) Use the Intermediate Value Theorem to show that f(x) has a root in the interval [3,4]. ii) Starting

Let f(x)=2x^2 + 5 - e^x

i) Use the Intermediate Value Theorem to show that f(x) has a root in the interval [3,4].

ii) Starting at x₀ = 3.5 , use the Newton's Method to find the root of the given equation, accurate to six decimal places, that lies in the given interval.

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