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The point A lies on the curve with the equation = 𝑥^1/2 . The tangent to this curve at A is parallel to the line 3𝑦 −2𝑥 = 1 . Find the equation of this tangent at A.

YEEEEEET Dec 2, 2018

#1**+1 **

The line will have the slope = 2/3

The derivative of x^(1/2) = 1 / ( 2√x)

So....to find the x coordiniate of A

2/3 = 1 / ( 2√x)

( 2√x) = 3/2 square both sides

4x = 9/4

x = 9/16

So....the y coordinate of A is (9/16)^1/2 = 3/4

And the equation of the tangent line is

y = (2/3) (x - 9/16) + 3/4

y = (2/3)x - 9/24 + 3/4

y = (2/3)x + 9/24

24y = 16x + 9

16x - 24y = -9

CPhill Dec 2, 2018