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A right triangle is changing shape. The base is increasing at the rate of 5 inches/sec while the height is the area changing? (A = ; bh) is increasing at a rate of 2 inches/sec. When the base is 4 inches and the height is 6 inches, how fast 6 : 5 inbec n- 2 bjh, dA = Zinlec dE = ( 2 se ) ( h ) ( 2 6 ) ( abt) dA Hin of = (2 ( 5)) ( 6) + ( 2 ( 4)) ( 2) oin dA ? at = 19 in/sec 5 The graph of f is shown below. Let g be the function given by g(x) = In (f (x)). Write an equation for the line tangent to the graph of g at x=3. g' (x)- Tx-5 (2) 9(3): In(218)-1)) ty 7Iflx ): 2 x - 1 g ( 3) = In (5 )! g'(3) = 5 (2) g ' ( 3 ) : I'm 4- In ( 5 ) = 2 ( x- 3 ) 6. Find an equation of a tangent line of h(x) = In (3x2 - 4) at x=2. h ( 2 )= In( 312)?-4) h' ( x ) = 3 x 21 ( GX ) or hi (x ) : 6x 3 x 2 4 h/2) = In ( 12-4) h' (2 ) . 6 (2 ) h / 2 ) = In 18 ) - 4 3 ( 2 ) 2 4 h ( 2 ) : - 3)= 32 ( x-2) h' (2 ) : 2 = m