Find the Tangent lines of the slopes of the three zeroes

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The discussion centers on finding the tangent lines of the slopes of the function defined as \( f(x) = 1 + \frac{50 \sin(x)}{x^2 + 3} \) within the interval -5 < x < 5. The three zeroes identified are approximately 0.02, 3.16, and -3.12. Participants emphasize the importance of applying the quotient rule for differentiation to find the slopes of the tangent lines at these zeroes.

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Nivetham
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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!
 
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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
 
Hi! It's the second equation. Thank you!
 
Nivetham said:
Hi! It's the second equation. Thank you!
Hello Nivetham,
Have you derivate the function?
Hint: Quotient rule

Regards,
 

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