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Task 1 In a coal company, the costs of extracting one tonne of raw lignite K (in 1000 () depending on the dirt mountain x to be conveyed and tilted (in m 3 ) accordingly the following function planned: K(X)= . Ln ( 2 where a is a positive real constant. 1. Find the first and second order derivatives of the cost function. 2. Investigate the monotony and curvature behavior of the cost function. For all of the following subtasks, set a = 0. 5 and the amount of spoil x o to 15 m 3 . 3. Determine and interpret the value K (x o ) of the marginal cost function. 4. By how many m 3 does the overburden amount have to be increased if with an approximate co- cost increase dk of only 1000 6 should be planned? 5. Determine and interpret the value s k x (x o ) of the elasticity of the cost function