Question

Find the slope of the curve at the given point.
9√x-7√y=29;(16,1)

Answer 1

To find the slope of the curve at the given point (16, 1) in the equation 9√x - 7√y = 29, take the derivative of the equation, evaluate it at x = 16 and y = 1, and solve for dy/dx. The slope of the curve at the point (16, 1) is 14/9.

Step-by-step explanation:

To find the slope of the curve at the given point (16, 1) in the equation 9√x - 7√y = 29, we need to take the derivative of the equation and evaluate it at x = 16 and y = 1. Let's start by taking the derivative of the equation with respect to x:

9/2√x - 7/(2√y) * dy/dx = 0

Simplifying the equation, we get:

9/2√x * dy/dx = 7/(2√y)

Now, we can substitute the values x = 16 and y = 1:

9/2√16 * dy/dx = 7/(2√1)

Simplifying further, we get:

9/8 * dy/dx = 7/2

Finally, solving for dy/dx, we have:

dy/dx = (7/2) / (9/8) = 56/18 = 14/9