This is Calculus and vector course for grade 12 high school.

Those are the questions I need help with and I also attached photo of formula sheet in case you need it as a reference. Those are three questions.

MCV4U - Grade 12 Calculus and Vectors Final Exam Formula Sheet Algebra Factoring Special Polynomials: x' ty' = (xty)(x2 F xy+ yz) Trigonometry Pythagorean Identity: sin x + cos' x =1 Factor Theorem: x - a is a factor of the polynomial Quotient Identity: sin x = tan x f(x) iff f(a) = 0 COSX Reciprocal Identities: Quadratic Formula: x = - - b+vb2 - 4ac cscx = - 2a Sin x 1 Logarithms sec x = cosx y = log. x a' =x cotx = log. a = 1, log. a* = x, dog* = x tan x log, x = In x Cofunction Identities: log, e = 1, Ine* = x, ex = x cosx = sin x+ ~ , sin x = cos x- Measurement Addition and Subtraction Formulas: Rectangular Prism: V = lwh, SA = 2lw+ 21h + 2wh sin(a + b) = sin a cosb + cosasin b sin(a - b) = sin a cosb - cosa sin b Cylinder: V = mr2h, SA = 272 + 2rrh cos(a + b) = cosa cosb - sin a sin b Cone: V = ~ nah, SA = 12 + mrs cos(a - b) = cosa cosb + sin a sin b tan(a + b) = = tan a + tan b , tan a tan b # 1 Sphere: V = ~ n , SA = 472 1 - tan a tan b tan(a -b) = tan a - tan b 1 + tan a tan b , tan a tan b # -1 Vectors a . b = lal|b|cose Double Angle Formulas: lax b| = lal|b|sine sin 2a = 2sin a cosa a cos2a = cosa -sin a a = lal cos2a = 2cosa-1 scalar proja onto b = lalcose cos2a =1-2sina vector proja onto b = lalcose tan 2a = - 2 tan a , tan a # +1 1 - tan a W = |d|F|cose y = sing(x)), y' = cos(g(x)) . g'(x) Area of a paralellogram = lax bl y = In(g(x) ), y' =- g ( x) 9 ( x ) Calculus Definition of the Derivative: f'(x) = lim f( x + h) - f(x) h - 0 h3. Let a = [3, -1,0], b = [-2,4,1]and c = [1,0, -2] find: [2K marks each] a) (2b) . (50) b) Vector Projection c onto b c ) ( b ) x ( C ) d) Unit vector of (b + c)5. Find the equations (more than one) of the tangents to the graph of f(x) = 2x3 + 3x2 - 6x Having a slope of 6 [3T+1C marks] 6. A cylindrical container, with a volume of 4000cm', is being constructed to hold candies. The cost of the base and lid is $0.5/cm , and the cost of the side walls is $0.25/cm2 . Determine the dimensions of the cheapest possible container. [3A+1Cmarks]