Determine equations of the lines tangent to

[krete77]

The problem is:
Tangent Lines: Determine equations of the lines tangent to the graph of Y = x√(5-x²) at the points (1,2) and (-2,-2). Graph the function and the tangent lines.

I have no IDEA where to go with this. I am taking calculus over the summer and we are in week 2 and I'm struggling..if anyone could do a step by step process here and explain I would be so grateful. Thanks in advance.

 

[HallsofIvy]

One of the first things you should have learned in Calculus is that the derivative of a function, at a given value of x, is the slope of the tangent line to the graph at that point on the graph. To find the slope of the tangent line at (2, 2) , find the derivative of y= x\sqrt{5- x^2} at x= 2, then use the "point-slope" formula for the equation of the line having that slope through the line (2, 2).