Test B Review, Calculator may be used, whichever is simpliest please show me thanks

Question

Answer 1

(31)

Two points on the gra[h are (0,$12) and (120, $0).

The lline equation when two points are known then (y-y₁)= m(x – x₁)

Slope

m = (0 - 12)/(120-0) = -12/120 = -0.1

Sustitute m = -0.1, x₁= 0 and y₁ = 12 in the point slope form of line equation.

(y-12)= -0.1(x – 0)

y = -0.1x + 12

Now the price per unit is $5

5 = -0.1x + 12

5 - 12 = -0.1x

-7 = -0.1x

x = 7/0.1

x = 70 units are sold in a week

Total Amount in a week = (Price per unit) * (Number of units sold) = 5 * 70 = 350

Therefore Total amount in a week when price per unit is $350.

Option (c) is the correct answer.

Answer 2

(32)

The function is f(x) = x^6 - x^4

Slope of the line f'(x) = -1

Apply derivative to the function f(x) with respect to x on both sides.

f'(x) = 6x^5 - 4x^3

Given that f'(x) = -1

6x^5 - 4x^3 = -1

6x^5 - 4x^3 - 1 = 0

Roots of the qudratic polynomial are -0.93355, 0.70483+0.238i, 0.70483-0.238i, -0.23806 + 0.51567i and -0.23806 - 0.51567i.

As we do not consider the imaginary values, so x = -0.93355

Substitute x = -0.93355 in f(x)

f(x) = (-0.93355)^6 - (-0.93355)^4

f(x) = -0.09759

So the point is (-0.93355, -0.09759)

The tangent line equation is in the form of y = mx + c

f'(x) = -1 and (-0.93355, -0.09759) passes through the line.

y = -x + c

-0.09759 = -(-0.93355) + c

c = -1.03114

then line equation is y= -x -1.031

Therefore the tangent line equation is   y = -x - 1.031.

Option (a) is the correct answer.