Question #0caf6

1 Answer
Feb 6, 2017

The curve has a slope of #-1# at #(2, 0)#.

Explanation:

The trick is to always remember you are differentiating with respect to #x# and to write "#dy/dx#" whenever you differentiate a different variable.

We differentiate the above equation using the power rule, which states that for a function #f(x) = x^n#, the derivative is given by #f'(x) = nx^(n - 1)#.

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

#x + 2y(dy/dx) + 2(dy/dx) = 0#

Solve for #dy/dx#

#2y(dy/dx) + 2(dy/dx) = -x#

#dy/dx(2y + 2) = -x#

#dy/dx = -x/(2y + 2)#

The slope of the curve at a point #x = a# can be obtained by evaluating #x= a# within #dy/dx#.

#dy/dx = -2/(2(0) +2)#

#dy/dx= -2/2#

#dy/dx= -1#

Hopefully this helps!