Question #1561c

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Answer 1 · 2016-10-22T02:00:31

Answer: #y=x+1/2#

Remember when we take the derivative of y, since there's a baby inside (y is a function of x), you need to also multiply it by y'

Step 1: Use implicit differentiation to find the derivative of the equation.

#2x+2yy'=2(2x^2+2y^2-x)(4x+4yy'-1)#

Step 2: Find the slope at (0, 1/2)

At (0, 1/2), plug in #x=0, y=1/2#
#2*0+y'=2(0+1/2)(0+2y'-1)#
#y'=2y'-1#
#y'=1#

At #(0,1/2)#, #m=1#

Step 3: Find the equation of the tangent line

#y-1/2=1(x-0)#
#y=x+1/2#

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