Help on this grade 12 calculus question?

Question

Determine the slope of the tangent to each curve at the given point.

a) √(x-7), (16, 3)

Answer 1

Step 1 :  

a)

The expression is and the point is .

The slope of the tangent line is equal to the derivative of the function at . 

Let .

Apply derivative on each side with respect to x. 

Step 2 :

Slope at the point :

Substitute  in  

The slope of the tangent line is .

Solution : 

a) The slope of the tangent line is .