Use Newton's method to approximate the indicated root of the equation correct to six decimal places.

Question

The negative root of e^x = 4 − x²

Answer 1

Let f(x) = e^x + x² - 4.

Now apply Newton's Method to that function by finding f'(x) = e^x+2x,

Looks like a starting value of -2 will get f(x) fairly close to a value of 0, so start with x₁ = -2.