The graph of x^2=-2+y+5cosy is shown for y=11 a.) find the derivative dy/dx b.)write an equation to the line tangent to the graph of point p. c.)find the y-coordinate of the graph where the line tangent to the graph at that point is vertical pls. show all your work and explain

(a)

We have been given an equation . Upon taking derivative of this equation with respect to x on both the sides, we get:

(b)

In order to write the equation of tangent line, we need to find the slope of the line. We know that point (3,11) lies on the graph. Therefore, we write the slope of the tangent as:

Therefore, equation of tangent line is:

(c)

We know that slope of tangent is given as . The tangent will be vertical when denominator of slope is zero, that is: