Lesson 14 Normal and Tangent Lines

# Lesson 14 Normal and Tangent Lines - Application 2 SLOPE...

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Application 2 SLOPE OF A CURVE, EQUATION OF THE TANGENT and NORMAL LINES

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OBJECTIV ES : determine the slope of a curve at a specified point; solve problems involving slope of a curve; determine the equations of tangent and normal lines using differentiation; and solve problems involving tangent and normal lines.
DEFINITION The derivative of at point P on the curve is equal to the slope of the tangent line at P, thus the derivative of the function f given by with respect to x at any x in its domain is defined as: ) ( x f y = ) ( x f y = 0 0 ( ) ( ) lim lim x x dy y f x x f x dx x x ∆ → ∆ → + ∆ - = = provided the limit exists . Recall:

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)) ( , ( 1 1 x f x P )) ( , ( 2 2 x f x Q ) ( x f y = x x x x x x + = - = 1 2 1 2 y tangent line secant line x y The derivative of a function is equal to the slope of the tangent line at any point along the curve.
( 29 . 6 , 1 at 1 x 2 x 3 y curve the of slope the Find . 1 2 - + - = 2 x 6 m 2 x 6 y : Solution line gent tan ' - = - = ( 29 ( 29 8 2 1 6 m : 6 , 1 at line gent tan - = - - = - EXAMPLE :

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( 29 ? 2 of slope have 1 x , 1 x 1 x y curve the do s int po what At . 2 - + - = ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29
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Lesson 14 Normal and Tangent Lines - Application 2 SLOPE...

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