The maximum occurs at x = 2, found by setting f'(x) = 4 - 2x = 0. f(2) = 4(2) - (2^2) = 4.

The function is a polynomial and is differentiable everywhere, hence nowhere.

The function is a polynomial and is differentiable everywhere. Thus, there are no points where it is not differentiable.

The product of the roots is given by c/a = 8/1 = 8.

The product of the roots is c/a = 9/1 = 9.

Factoring gives (x + 4)(x - 2) = 0, hence the roots are -4 and 2.

This is a perfect square: (x + 3)² = 0, hence the root is x = -3.

Scalar product = 0*3 + 1*4 + 2*5 = 0 + 4 + 10 = 14.

A · B = 1*2 + 1*2 + 1*2 = 2 + 2 + 2 = 6.

A · B = 2*3 + 2*3 + 2*3 = 6 + 6 + 6 = 18.

f'(x) = 2x; thus, f'(3) = 2(3) = 6.

-2x + 6 > 0 => -2x > -6 => x < 3.

-2x + 6 ≥ 0 => -2x ≥ -6 => x ≤ 3.

-3x + 1 ≤ 4 => -3x ≤ 3 => x ≥ -1.

-3x + 4 ≤ 1 => -3x ≤ -3 => x ≥ 1.

2x + 3 ≤ 7 => 2x ≤ 4 => x ≤ 2.

6 - x > 2 => -x > -4 => x < 4.

6 - x ≤ 3 => -x ≤ -3 => x ≥ 3.

7 - 3x < 1 => -3x < -6 => x > 2.

7x - 2 ≤ 5x + 6 => 2x ≤ 8 => x ≤ 4.

This is separable. Separating and integrating gives y = 1/(C - x).

2(x - 1) ≥ 3 => x - 1 ≥ 1.5 => x ≥ 2.

2x + 3 > 5 => 2x > 2 => x > 1.

2x + 3 > 7 => 2x > 4 => x > 2.

2x + 3 ≤ 7 => 2x ≤ 4 => x ≤ 2.

3x - 4 < 2x + 5 => x < 9.

4x - 1 > 3 => 4x > 4 => x > 1.

4x - 1 > 3x + 2 => x > 3.

4x - 1 < 3 => 4x < 4 => x < 1.

4x - 8 < 0 => 4x < 8 => x < 2.