Assign.#2Sol. - Problem 3: [4 points] Give the equation of...

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Problem 3: [4 points] Give the equation of the tangent line to the curve y = sin(sin( x )) at ( x,y ) = ( π, 0) . Solution: The equation of the tangent line at ( x,y ) = ( π, 0) is y = f ( π ) + f 0 ( pi )( x - π ) . f 0 ( x ) = cos(sin( x ))cos( x ) ,f 0 ( π ) = - 1 , and f ( π ) = 0 . Hence the equation of the tangent line to the curve y = sin(sin( x )) at ( x,y ) = ( π, 0) is y = - ( x - π ) = - x + π . Problem 4: [6 points] Use the first and second order derivatives to sketch the graph of f ( x ) = x + 4 x 2 . You have to find the critical points, inflexion points, intervals where the function is increasing, . .., and the vertical and horizontal asymptotes if any. solution: f ( x ) = x + 4 x 2 , f 0 ( x ) = 1 - 8 x 3 et f 00 ( x ) = 24 x 4 . The function f does not defined at x = 0 , and is positive for x > - 4 1 / 3 and negative for x < - 4 1 / 3 . The derivative of the function f does not exist at x = 0 and f 0 ( x ) = 0 x = 2 . This implies the function has two critical points at
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Assign.#2Sol. - Problem 3: [4 points] Give the equation of...

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