How do you find an equation of the tangent line to the curve #y = arcsin(x/2)# at the point where #x = −sqrt2#?

1 Answer
bp
Apr 13, 2015

First find the derivative of arcsin#(x/2)#. It would be #1/2# #1/sqrt(1-x^2/4)#. This would give the slope of the tangent line at any given point of which x coordinate is known. In the present case it is x= -#sqrt2#.

The slope would accordingly be #1/2# #1/sqrt(1-2/4)# = #1/sqrt2#.

For x= -#sqrt2#, y= arcsin#(-sqrt2 /2)# = #-pi/4#.

Equation of tangent line, in the point slope form, would be y+#pi/4#= #1/sqrt2# ( x +#sqrt2)#

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