Maxima and Minima Maths - Maxima and Minima

If x + y = 8, then the maximum value of xy is:

1. 8
   
2. 16
   
3. 20
   
4. 24
   

Let f(x) = 2x³  - 3x² - 12x + 5 on [-2, 4]. The relative maximum occurs at x =

1. -2
   
2. -1
   
3. 2
   
4. 4
   

If f(x) attains a local minimum at x = c, then write the values of f' (c) and f'' (c).

Write sufficient condition for a point x = c to be an extreme point of the function f(x).

Write necessary condition for a point x = c to be an extreme point of the function f(x).

Find the points o local maxima or local minima, if any, of the following functions, using the first derivatives test. Also, find the local maximum or local minimum values, as the case may be:
f(x) = x³ - 3x