Find the points of local maxima and local minima of f(x) = x³ – 6x² + 9x + 2014, x ε

Solve the inequality   5and graph its solution.

A tailor needs at lease 40 large buttons and 60 small buttons. In the market, buttions are available in two boxes or cards. A box contains 6 large and 2 small buttons and a card contains 2 large and 4 small buttons. If the cost of a box is $3 and cost of a card is $ 2, find how many boxes and cards should be purchased so as to minimize the expenditure.

If α, β are roots of x² – 3ax + a² = 0, find the value(s) of a if α² + β² =  .

Determine the values of x for which f(x) = x ⁴ – 8x ³ + 22x ² – 24x + 21 is increasing and for which it is decreasing.

Using integration, find length of the curve y = 3 – x from (-1, 4) to (3, 0)

Show that A² - 4 A + 5 I₂ = 0. Also, find A⁴ .