please show me how to do them, I am allow to use a calculator for this part

Question

Answer 1

20.

The Profit function at x units is .

Apply Derivative on each side.

The marginal function at x = 100

The Marginal Profit is 49.4.

Answer 2

22.

The cost function is where x > 0.

Marginal cost is zero then c(x) = 0.Apply differention on each side.

 

Therefore x=3/2 when marginal cost is zero.

Answer 3

The Function is .

To find the slope of tangent line, derivative with respect to x to the above function

f'(x) = 12x³ + 6x² - 108x -210.

12x³ + 6x² - 108x -210 = 0

(x-3.5)(x+2-i)(x+2+i) = 0

x = 3.5, -2-i, -2+i.

Point for the tangent line is positve value.Imaginary points are not considered.

At x = 3.5,

y = -860.4625

Therefore the Tangent Point is (3.5, -860.46).

The Graph is given as

Therefore the tangent point is (3.5, -860.46).