MHB Find the Tangent lines of the slopes of the three zeroes

[Nivetham]

1+50sinx/x^2+3
-5 < x < 5

3 zeroes: 0.02, 3.16, -3.12
Find the derivative and the slopes of the tangent lines.

I need help with the last part. I found out the three zeroes by adding and subtracting pi from the equation at top by setting it to zero.
Thank you!

 

[Jameson]

Hi Nivetham,

Welcome to MHB! :)

Is this your equation? $$f(x)=1+\frac{50 \sin(x)}{x^2}+3?$$ or is it $$f(x)=1+\frac{50 \sin(x)}{x^2+3}$$, or is it $$\frac{1+50 \sin(x)}{x^2+1}$$?

Jameson

 

[Nivetham]

Hi! It's the second equation. Thank you!

 

[Petrus]

Hi! It's the second equation. Thank you!

Hello Nivetham,
Have you derivate the function?
Hint: Quotient rule

Regards,