# 0119 - Math 31A 2010.01.19 MATH 31A DISCUSSION JED YANG 1...

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Unformatted text preview: Math 31A 2010.01.19 MATH 31A DISCUSSION JED YANG 1. Derivatives 1.1. Basics. Given a function f ( x ). The slope of the tangent line at x = c is f ′ ( c ). 1.1.1. Power Rule. For all exponents n ∈ R , d dx x n = nx n − 1 . Not for e x , x x . 1.1.2. Linearity Rules. If f and g are differentiable functions, c ∈ R , then cf and f + g are differentiable. Indeed, ( f + g ) ′ = f ′ + g ′ and ( cf ) ′ = cf ′ . 1.1.3. Product and Quotient Rules. If f and g are differentiable, ( fg ) ′ = fg ′ + gf ′ . And ( f/g ) ′ = ( f ′ g − g ′ f ) /g 2 . 1.2. Exercise 3.2.46. Sketch the graphs of f ( x ) = x 2 − 5 x +4 and g ( x ) = − 2 x +3. Find the value of x at which the graphs have parallel tangent lines. Solution. We need f ′ ( x ) = g ′ ( x ). Notice f ′ ( x ) = 2 x − 5 and g ′ ( x ) = − 2. So we solve 2 x − 5 = − 2 to get x = 3 2 . square 1.3. Exercise 3.2.52. Show that if the tangent lines to the graph of y = 1 3 x 3 − x 2 at x = a and x = b are parallel, then either...
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## This note was uploaded on 09/19/2011 for the course MATH 31A taught by Professor Jonathanrogawski during the Winter '07 term at UCLA.

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0119 - Math 31A 2010.01.19 MATH 31A DISCUSSION JED YANG 1...

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