86.6k views
0 votes
Question content area top part 1 differentiate implicitly to find . then find the slope of the curve at the given point. ​0; ​(​,​)

User Stanga
by
7.5k points

1 Answer

1 vote

Final answer:

To find the slope of a curve at a given point using implicit differentiation, we differentiate the equation with respect to x, solve for the derivative, and substitute the given point to find the slope.

Step-by-step explanation:

Implicit differentiation

To find the slope of the curve at the given point, we need to differentiate the equation implicitly. Let's say the equation of the curve is represented by y=f(x). To find the derivative dy/dx, we differentiate both sides of the equation with respect to x, treating y as a function of x.

Next, we solve the resulting equation for dy/dx to find the derivative. Once we have the derivative, we can substitute the x-coordinate of the given point to find the slope of the curve at that point.

Example:

Let's say the equation is x^2 + y^2 = 9 and we want to find the slope of the curve at the point (3, 0). The first step is to differentiate both sides with respect to x, treating y as a function of x:

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

Now, we can solve this equation for dy/dx:

dy/dx = -x/y

Substituting the x-coordinate (3) and y-coordinate (0) of the given point into the derivative, we find that the slope at the point (3, 0) is 0.

User Eric Majerus
by
8.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories