Math1011_Week07_3_678 - Math1011 Learning Strategies Center...

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Unformatted text preview: Math1011 Learning Strategies Center Section 3.6 10/24/2009 Find the slope of circle x 2 + y 2 = 25 at point (3,-4). Use implicit differentiation to show that the circle x 2 + y 2 =25 is concave down in 2nd quadrant. Note: to show f(x) is concave down, show f(x) < 0. Math1011 Learning Strategies Center Section 3.6 10/24/2009 Find the slope of circle x 2 + y 2 = 25 at point (-3,4). 2 2 d d d dx dx dx d d dx dx 2 2 3 3 4 4 x 25 Implicit Differentiation and Chain Rule 2 ( x ) 2 ( ) 2 2 2 2 (-3, 4), The slope on the circle on (-3, 4) is 3/4. dy dx dy dx dy x x y y dx dy x y dx y x y y x y y x At + = + = + = = = = = = = Use implicit differentiation to show that the circle x 2 + y 2 =25 is concave down in 2nd quadrant. Note: to show f(x) is concave down, show f(x) < 0. 2 2 2-x y ( 1) ' '' ( ) Take 2nd derivative ( ) ( ) '' Quotient Rule ( 1) ' '' 2nd quadrant: y > 0 and x < 0 so y'= '' As y''< 0, y is concave down in 2nd qua d x y dx d d dx dx y x y y y y x x y y y y x y y y y + = = + = > = < drant (Doc #011w.36.01t) Math1011 Section 3.6 2 2 2 Consider the curve x y - 6y + 2 = 0 Find the equation of the tangent line to the curve at point (2,1) Math1011 Section 3.6 2 2 2 Consider the curve x y - 6y + 2 = 0 Find the equation of the tangent line to the curve at point (2,1) 2 2 2 2 2 2 d d d d dx dx dx dx 2 2 2 2 2 2 2 2 2 2 2 2...
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Math1011_Week07_3_678 - Math1011 Learning Strategies Center...

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