The Cost Function Fi A company's cost function is C(x) = 4 - x2 + 2 - x + 125. a) Find the average cost function. C(x) = The feedback must read "The variables found in your answer were: [x]" otherwise your grade will be 0. b) Find the marginal cost function. C' (x) = The feedback must read "The variables found in your answer were: [x]" otherwise your grade will be 0. c) Use the marginal cost function to estimate the cost of producing the 6th item. (place the correct integer in the box) The estimated cost of producing the 6th item is: . CheckTime left 0: We can use the Intermediate Value Theorem to show that the following equation has a solution: In (3 . z) = e 5.1 Step 1: Solve this equation for 0. By subtracting the right hand side on both sides of the equation we get: Now define a function f with the left hand side of the equation: f(I) Step 2: State the domain of f (x). The domain in interval notation is. Step 3: Find a continuous interval a, b] of f() so that f( a) is negative and f (b) is positive. The function f(z) is continuous on a, b). (No answer given) - We now conclude by the Intermediate Value Theorem that the function f has a root (crosses the x-axis) in the interval (a, b) so the original equation has a solution. CheckUse the linearization of f(x) - 37 at 4 to to estimate: 34.005 a) What is the slope of the tangent line of f(x) = 3 when z - 4? The slope is: b) Find the linearization of f at 4. In other words, find the equation of the tangent line for f(x ) = 37 at x = 4. L(x) The feedback must read "The variables found in your answer were: [x]" otherwise your grade will be 0 for this part. c) Use the tangent line to find the estimate of 31-005 L( 4 + 5 1000 The estimation is: 34,005 Checkb) g(I) = ez I24 1 g' ( t ) = c) h(I) = (4 . 1+5) 4145 h' ( t ) = In each part the feedback must read "The variables found in your answer were: [x]" otherwise your grade will bmit lim el(1-z?) Answer xists enter the correct real number in the box. If the limit goes to co enter "inf. If the limit goes to -inf". If the limit does not exist for any other reason enter "DNE&quot