Finding Value of k for Tangent to y=\frac{3x}{\sqrt{1+x}} at x=3

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To find the value of k for the tangent to the curve y=3x/√(1+x) at x=3, first calculate the y-coordinate by substituting x=3 into the curve equation, yielding y=3. Next, determine the slope of the tangent line using calculus, which involves finding the derivative of the curve. The slope of the line given by 15x - 16y = k can be derived from its standard form, leading to a slope of 15/16. By equating the slopes and using the point (3,3), the value of k can be calculated. The final result provides the necessary value of k for the tangent line.
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Homework Statement


The equation of a curve is y=\frac{3x}{\sqrt{1+x}}.
Given that the equation of the tangent to the curve at the point x=3 us 15x-16y=k , find the value of k. SOLVED

Homework Equations


The Attempt at a Solution

 
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Do you know the y-coordinate on the curve when x = 3?
Do you know how to find the slope of a curve (i.e., the slope of the tangent line to the curve)?
Do you know how to find the slope of the line 15x - 16y = k?
 

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