Question

Calculate two iterations of Newton's Method to approximate a zero of the function using the given initial guess. (Round your answers to three decimal places.)

45. f(x) = x⁵ − 5,    x₁ = 1.4

n	xn	f(xn)	f '(xn)	f(xn) f '(xn)	xn − f(xn) f '(xn)
1
2

40. Find two positive numbers satisfying the given requirements.

The product is 234 and the sum is a minimum.

smaller value=

larger value=

30.Determine the open intervals on which the graph is concave upward or concave downward. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

y = 2x + 7/sinx ,    (−π, π)

concave upward:

concave downward:

4.Find the points on the graph of the function that are closest to the given point.

f(x) = x² − 8,(0, −5)

(x,y)= ( , ) (Smaller X-value)

(x,y)= ( , ) (Larger X-value)

Answer 1

45) and 40)

30)

concave upward:

concave downward:

4)