(a) Explain how we know that the given equation must have a root in the given interval. (b) Use Newton's method to approximate the root correct to six decimal places.
$ -2x^5 + 9x^4 - 7x^3 - 11x = 0 $, $[3, 4] $
a) Use the IVT to explain how there must be at least one root
b) $x \approx 3.274473$
okay, Part A. We know the intermediate value theorem states There must be at least 10 on the interval three or four because the function takes on every value between negative 236 and 21 including zero for part B. We know that can differentiate. So now we know X one is 3.2. Therefore, X two is 3.2, minus half of 3.2 over a prime of 3.2, which is approximately 3.284 Repeat the same process for X three. We got 3.275 x four. We get 3.274 and we get X 53.274 It's at this point that we know are Axe is gonna be approximately three 0.2744 73