c10s2 - the parameter first for 5cos , 5sin x t y t = = ....

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10.2 Tangents and Areas If we have parametric equations  x=f(t) , y=g(t) and we substitute y=F( x ), then we have g(t)=F( f(t)) . Now, if g,F, and f are  differentiable functions, the Chain Rule can be used to find g’(t). '( ) '( ) '( ( )) '( ) '( ) '( ) '( ) '( ) Slope of the tangent to ( ) at ( , ( )) is '( ) 0 g t g t F f t f t F x f t F x f t y F x x F x F x dy dy dx dt dx dx dt dt = = = = = Example: Find an equation of the tangent line at t=1 for the curve   3 2 1 , 3 1 x t y t t = - = - + . Example: Find an equation of the tangent to the curve at (3,4)  (a)  without eliminating the parameter and (b)  by eliminating 
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Unformatted text preview: the parameter first for 5cos , 5sin x t y t = = . The second derivative can be used to find concavity. 2 2 d dy d y d dy dt dx dx dx dx dx dt = = Example: Find the second derivative for 2cos , sin 2 x t t y t = + = . Example: Find the points on the curve where the tangent is horizontal or vertical for 3 2 3 3 , 3 x t t y t t =-=-....
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