Find the derivative. y = 57x A) 7 ( In 5) 57x O B) 35 (In 7) 57x O C) 35 (In 5) 57x O D) 5 (In 7) 57xUse the properties of limits to help decide whether the limit exists. If the limit exists, find its value. 4x3 + 5x lim X-60 -6x4 + 8x3+10 A) O (B) 1 O c - O D) .Determine all critical points for the function. f(x) = x3 - 12x + 5 O A) x = 2 O B) x = -2, x = 0, and x = 2 O C) x = - 2 O D) x = -2 and x = 2Solve the problem. From a thin piece of cardboard 10 in. by 10 in., square corners are cut out so that the sides can be folded up to make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? Round to the nearest tenth, if necessary. O A) 6.7 in. x 6.7 in. x 1.7 in.; 74.1 in3 ( B) 3.3 in. x 3.3 in. x 3.3 in.; 37 in 3 O C) 6.7 in. x 6.7 in. x 3.3 in.; 148.1 in3 O D) 5 in. x 5 in. x 2.5 in.; 62.5 in 3Evaluate the definite integral. Round your answer, if necessary. (x2 + 1) dx -1 O A) 2.67 O B) -.67 O C) - 2.67 O DJ OUse I'Hopital's Rule to evaluate the limit. x3-7x2+6 lim x - 1 x-1 O A) 14 O B) -11 O C) 17 O D) 10