In order to find the instantenous velocity the derivative of the function must be taken. This is equal to 3t² + 2t + 1. The velocity at this instant is equal to the value found when t=2 is plugged in: (3*2²)+ (2*2) + 1 = 12 + 4 + 1= 17(metre/seconds). The answer is B.

P(x) = R(x) – C(x) ; R(x) = (30 – (x / 4)) x ; P(x) = -0.25 x² + 27 x – 600 ; P'(x) = -0.5 x + 27 = 0 ; x = 54 ; P(54) = 27² – 600 = 729 – 600 = 129. pg. 164. Correct answer is B.

For the extreme points the first derivative must be equal to zero. Since f(x)=x³-4x The first derivative of function f(x) will be:

f'(x)=3x²-4

Then we find the roots of the f'(x) as following:

3x²-4=0

3x²=4

x= -√ 2/3 and x= √ 2/3 are the roots of this equation. So the answer is D.

L(x, y, λ )= x – y + λ (x² – 2 y² − 10) ; ∂L / ∂x = 1 + 2 λ x = 0 ; λ = -1 / (2 x) ; ∂L / ∂y = -1 – 4 λ y = 0 ; λ = -1 / (4 y) ; 2 x = 4 y ; x = 2 y ; ∂L / ∂λ = 0 ; x² – 2 y² = 10 ; (2 y)² – 2 y² = 10 ; 2 y² = 10 ; y = {-5^1/2 , 5^1/2}; x = {-2 5^1/2 , 2 5^1/2} ; f(x, y) = x – y = 5^1/2 > 0. pg. 193. Correct answer is D.

Let us write the demand function for q

q=1750-5p

Taking the derivative with respect to p we get

dq/dp = -5

The price elasticity of demand is

From this equation we can easily write the price for the unit elasticity which is 

1=5p/(1750-5p)

and the sought for price is p=175. Therefore, the answer is A.

We first find the equilibrium point by equating the supply and demand functions. Therefore, the equality 

-5x+500=2x-200

gives

7x=700,   x=100

Since there will be a shortage in the market, to the left o this point the correct answer x<100. The answer is E.

f(t) = 3t² -2t

so:

f(6)=3*6² -2*6=96

f(4)=3*4² -2*4=40

Average velocity(4,6)=(f(6)-f(4))/(6-4)=(96-40)/2=28

There is no need to calculation. Since f_xy=f_yx, f_xy-f_yx=0

The answer is B.

The price of a product at the intersection point, provided that it is in the first quadrant, is called market price. We may easily find that the market price of the ne TV in question. 

x is found as 50. When we put it on the demand or supply equations, we find market price as 125. 

E ∪ G = {x| x is a tourist who can speak English or German}

E ∩ G = {x| x is a tourist who can speak both English and German}

Then

s(E ∪ G) = s(E) + s(G) – s(E ∩ G)= 10 + 15 – 9 = 16.

Since a rational function f is continuous on the domain of its definition, f is continuous on its domain. This function is continuous for all real numbers except 3 which makes its denominator 0. Hence, the set of continuity of this function is R \ {3}. 

 The answer is D.

?f / ?x = 4x+ 2y-6         ?f / ?y=2x+4y

for the critical points;

4x+ 2y-6=0 and  2x+4y=0, so x=2, y=-1.

?²f / ?x² =4         ?²f / ?y² =4       ?f / ?xy =2

D=4.4-2²=12.

Since D>0, the function has a local minimum at (2,-1).

f(x)=6x² - x – 1

f'(x)=12x – 1

for x=0,  f'(x)= – 1

and the output of the function at x=-1 is f(-1)=6(-1)² -(-1)– 1=6

The point is (-1,6)

The average velocity is defined by v_av=(f(t₂)-f(t₁))/(t₂-t₁). So we have to calculate f(t) for t=1 and for t=3.

f(t)=5t²-2t+1

f(3)=45-6+1=40

f(1)=5-2+1=4

Then, v_av=(f(t₂)-f(t₁))/(t₂-t₁)=(40-4)/(3-1)=18 for interval [1,3].

The inequality  should be satisfied. Hence, we conclude 6x. 

D_f = (-∞, 6], so the correct answer is A.

dz/du=(dz/dx)*(dx/du)+(dz/dy)*(dy/du)

Since z=(x+y)², dz/dx=2x+2y and dz/dy=2x+2y 

Since y=u³, dy/du=3u²

x=u²-u, dx/du=2u-1

By substitution

dz/du=(2x+2y)(2u-1)+(2x+2y)3u²=(2x+3y)(3u²+2u-1)=(2(u²-u)+3u³)(3u²+2u-1)=(2u²-2u+3u³)(3u²+2u-1)=9u⁵+12u⁴-5u³-6u²+2u