Question

If y is a differentiable function of x, then the slope of the tangent to the curve xy-2y+4y^2 =6 at the pint where y=1 is:
(a) 1/12 (b)-1/10 (c) -1/6 (d) 1/4 (e) -5/6

Answer 1

\[\huge {\color{DarkRed} {\frac{-1}{10}}}\]

Answer 2

You would have to implicitly derive this function and then plug 1 into the derivaitve

Answer 3

thank you. and once the implicit derivation is done, what do i do

Answer 4

Solve\[x* y-2*y+4 y^2-6==0\]for y. There are two solutions. The one we want is:\[y=\frac{1}{8} \left(2-x+\sqrt{100-4 x+x^2}\right)\]Evaluate the original expression at y = 1. The associated x = 4. The derivative of the above is:\[\frac{1}{8} \left(-1+\frac{-4+2 x}{2 \sqrt{100-4 x+x^2}}\right) \]The above evauated at x=4 is\[-\frac{1}{10} \]A plot is attached.