Question

the point of inflection of f(x)=x^6 is​

Answer 1

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

For point of inflexion the function has neither maxima nor minima this is called point of inflexion.

Concept

Here ,f(x) is given so,we first find its derivative and make equal to zero and hence find value of x and then find its double derivatives and put value of x here.If the function is greater than zero then it's minima or if less than zero then it's maxima or if zero comes then it's point of inflexion.

↦f(x)= x⁶

finding derivatives

↦f'(x) or dy/dx = 6x⁵

↦f'(x)=0

↦6x⁵=0

↦x⁵=0

↦x=0

finding second derivatives

↦f"(x)= 6×5x⁴

↦f"(x)= 30x⁴

put x=0

f"(x) at x=0

↦30(0)⁴=0

Zero signifies point of inflexion.

Hence,the function is point of inflexion at x=0.

Answer 2

Answer:

f(x)= x⁶

finding derivatives

f'(x) or dy/dx = 6x⁵

f'(x)=0

6x⁵=0

x⁵=0

x=0

finding second derivatives

f"(x)= 6×5x⁴

f"(x)= 30x⁴

put x=0

f"(x) at x=0

30(0)⁴=0

Zero signifies point of inflexion.

Hence,the function is point of inflexion at x=0.