Downloaded 31 times
Uploaded bykliegey524
PPT, PDF2,717 views
Implicit Differentiation, Part Ii
The document discusses implicit differentiation and how to determine where the slope of a curve is undefined or zero. It provides examples of using implicit differentiation to find the slope (dy/dx), points where the slope is undefined by setting the denominator equal to 0, and points where the slope is zero by setting the numerator equal to 0. The document also gives steps to find the point where a normal line to a curve intersects that same curve.
More Related Content
What's hot
Similar to Implicit Differentiation, Part Ii
More from kliegey524
Recently uploaded
Implicit Differentiation, Part Ii
- 1.
- 2. Differentiate x 2+4xy+4y 2 -3x=6
- 3. How do wedetermine where the slope of the curve is undefined? Ex. 1 Determine where the slope of x 2 +4xy+4y 2 -3x=6 is undefined. -4x- 8y=0 -4x = 8y - ½ x = y or x = - 2y (any point where y = - ½ x) Steps Find dy/dx Set denominator = 0 Solve for x or y
- 4. How do weuse implicit differentiation to find Determine of y 2 +2y = 2x + 1 Steps Find dy/dx Use implicit differentiation on dy/dx to find Where dy/dx occurs, substitute the dy/dx found in step 1 Simplify
- 5. Find the pointson the curve x 2 + xy + y 2 = 7 a) where the tangent is parallel to the y-axis and (undefined) b) where the tangent is parallel to the x-axis (zero) Steps Find dy/dx If looking for undefined: set denominator = 0 If looking for zero slope, set numerator = 0
- 6. The line thatis normal to the curve x 2 + 2xy – 3y 2 = 0 at (1,1) intersects the curve at what other point? Steps Find dy/dx Find the equation of the normal Solve the normal for y Sub y back into the original equation and solve for x Get y to go with x from normal