Question

Carry out the following steps for the given curve.

a. Use implicit differentiation to find dy/dx.
b. Find the slope of the curve at the given point.x²+y²=5 ;(1,-2)

Answer 1

To find dy/dx for the given curve, we use implicit differentiation. The slope of the curve at the point (1, -2) is 1/2.

Step-by-step explanation:

To find dy/dx for the given curve, we first need to use implicit differentiation. We differentiate both sides of the equation x²+y²=5 with respect to x.

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

Now, we can solve for dy/dx by isolating it:

dy/dx = -2x/2y

Simplifying further:

dy/dx = -x/y

To find the slope of the curve at the given point (1, -2), we substitute x=1 and y=-2 into the equation dy/dx = -x/y:

dy/dx = -1/-2 = 1/2

Therefore, the slope of the curve at the point (1, -2) is 1/2.