Question

What are the points of inflection of #f(x)=1/(5x^2+3x) #?

Answer 1

No Points of inflection

Explanation:

Writing
`f(x)=(5x^2+3x)^(-1)`
So
`f'(x)=-(5x^2+3x)^(-2)(10x+3)`
`f'(x)=-(10x+3)/(5x^2+3x)^2`
Using the Quotient rule to get

`f''(x)=-(10(5x^2+3x)^2-(10x+3)*2*(5x^2+3x)*(10x+3))/(5x^2+3x)^4`

Simplifying we get

`f''(x)=(6(25x^2+15x+3))/(x^2*(5x+3)^2)`