Ap calc 98 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

Looking at this question again, I don't understand why you're told "for y=11". That doesn't seem relevant at all... So you can disregard the answer I posted a few minutes ago on your other question.

a) With , differentiate both sides with respect to to get

b) The point P occurs at , which corresponds to a -coordinate of

The slope of the line tangent to this point is approximately

so the equation of the tangent line is approximately

c) The tangent line to the graphed curve is vertical when is undefined. This happens when , or and where is any integer.

In case you're not sure where the general solution came from: We have

which has an infinite number of solutions. is one of them, which we obtain by taking the inverse sine of both sides of this equation. Since , we also know that is a solution. And since for integers , we also know that we can add any multiple of to these two solutions to get infinitely more solutions.

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step-by-step explanation: