Find the equation of the tangent line to the curve 𝑦=𝑥‾‾√ at the point (9,3), then sketch the graph of the curve and the tangent line to confirm your answer.First find the slope of the tangent line:

To find the equation of the tangent line to the curve y = √x at the point (9,3), we first need to find the derivative of the function y = √x.

The derivative of y = √x is given by:

dy/dx = 1/(2√x)

Now, we can find the slope of the tangent line at the point (9,3) by substituting x = 9 into the derivative:

m = 1/(2√9) = 1/6

So, the slope of the tangent line at the point (9,3) is 1/6.

Next, we can find the equation of the tangent line using the point-slope form of a line, which is given by:

y - y1 = m(x - x1)

Substituting m = 1/6, x1 = 9, and y1 = 3, we get:

y - 3 = 1/6(x - 9)

This simplifies to:

y = 1/6x + 1

So, the equation of the tangent line to the curve y = √x at the point (9,3) is y = 1/6x + 1.

To confirm this, you can sketch the graph of the curve y = √x and the line y = 1/6x + 1. You should see that the line is tangent to the curve at the point (9,3).