Pls answer all given questions asap on paper with neat handwriting and showing/explaing all steps to answer

For each of the following find the first and the second derivative. x +1 y = vcosx Question-10 For each case, find any local extrema using the first derivative test for the first function and absolute extrema and points of infection for the second function in the given interval. S(x)=x-2x2+1 f(x) = x + sinx, for xe[0,2x] Question-11 Sketch the graph of the following functions using algorithm for curve sketching. f(x)=3x5-5x3 f ( x) = 2 x2 - 1 if 2 2700cm of material is available to make a box with a square base and open top, find the dimensions of the box that give Question-12 the largest volume of the box. What is the maximum value of the volume? Given a =(-1,2,-3) , b =27 - ] + k , and c=7 + ] Question-13 Find v = 2a - b + 3c, and unit vector along of v. Question-14 For what values of k are the vectors a = (6,3, -4) and b = (3, k, -2) Perpendicular (orthogonal) parallel (colinear) Question-15 Find the angle between the vectors a = (1, -2. -1)and b = (0, -2,1) Question-16 Given two vectors a =(0,1,-2) and b =(-1,0,3) , find: Vector projection of b onto a. Scalar projection of a onto the vector i - j Question-17 Consider the following vectors: a =i + j-k , b =3i -2j , and =3i -2k . Compute the required operations in terms of the unit vectors i , j , and k . (axb ) . c (axb ) xc