Question

A function is defined by
y= x^3/48 + 1/x

(A) Find dy/dx
- my answer: 1/16x^2-x^-2

(B) Find d^2y/dx^2
- my answer: 1/8x+2x^-3

C) use your answer to (A) to find the x coordinate of the two stationary points.

D) use your answer to (B) to determine whether each point is a maximum or a minimum

Please help
Thankyou :)

Answer 1

C)
the function graph is horizontal when dy/dx = 0

(1/16) x^2 -1/x^2 = 0

(1/16) x^4 = 1
x^4 = 16

x = + or - 2

D)
at x = -2
d^2y/dx^2 = (1/8)(-2) +2(1/-8)
negative so headed down, a maximum
at x = + 2
POSITIVE SO HEADED UP, MINIMUM