Question

Find the intervals in which the function f given by f(x)=x^3+1/x^3 ,x≠0 is (i) increasing (ii) decreasing

Answer 1

HELLO DEAR,

GIVEN:- f(x) = x³ + 1/x³

( 1 ) . now, f'(x) = dy/dx(x³ + x^{-3})

= $\bold{(3x^2 - 3x^{-4})}$

= (3x² - 3/x⁴)

f'(x) = 3(x² - 1/x⁴)


( 2 ). now put f'(x) = 0

3(x² - 1/x⁴) = 0

x² - 1/x⁴ = 0

(x^6 - 1)/x⁴ = 0

x^6 = 1

x = ±1

HENCE, x = 1 , x = -1

thus value of x = - 1 & 1
i.e. f(x) is strictly increasing on ( -∞ , - 1) & (1 , ∞)
and strictly deacreasing on (- 1 , 1)


I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Answer:

Step-by-step explanation:

Hope you understood.