f(x)=-x²+13x-27

 f'(x)=-2x+13

 f'(5)=-2.5+13=3.

(x + 2) / (x + 2) = 1 . pg. 109. Correct answer is C.

The break-even point is the point at which cost or expenses and revenue are equal: so;

Cost: 300x+12000

Revenue : 500x

300x+12000=500x, then x=120. 

lim_x→5^- ( x-7 / x - 5) = -2 / 0^- = +∞.

lim_x→5⁺ ( x-7 / x - 5) = -2 / 0⁺ = -∞.

The limit of the function at x = 5 does not exist due to the different behaviour of one-sided limits. 

For the function  x³ + 2x² - 4x the derivative is equal to 3x² + 4x - 4 and the second derivative is equal to 6x + 4. If we equal the derivative functions to zero we would have  3x² + 4x - 4=0 is (3x-2)(x+2)=0 x will be equal to -2 and 2/3, these are the critical points. When we plug each one to the second derivative we will find 6(-2)+4=-8 and 6(2/3)+4=8. -8<0 which makes x=-2 a local maximum and 8>0 which makes x=2/3 a local minimum. The answer is D.

The answer is C.

Q(t) = Q₀ e^{k t} ; 0.9 Q0 = Q⁰ e^{k 25} ; ln 0.9 = k 25 ; k = (ln 0.9) / 25 ; 0.5 Q₀ = Q₀ e^{((ln 0.9) / 25) t} ; ln 0.5 = ((ln 0.9) / 25) t ; t = 25 (ln 0.5) / ln 0.9 . Correct answer is C.

x = ((1 / 5) + (1 / 2))^-1 / ((1 / 5) – (1 / 2))^-1 = -3 / 7. Correct answer is A.

p : price ; x : quantity ; at equilibrium : 1.200 – 3 x = 5 x – 400 ; 1.600 = 8 x ; x = 200 ; p = 600. pg. 160. Correct answer is A.

The answer is B.

f(x,y)=5+e^-3y+x.lnx

?f/?x=(x.lnx)'=x'.lnx+x.lnx'

=lnx+1

The function is a rational function. Since the degree of the numerator is greater than the degree of the denominator, the following result is;

The answer is D.

∞ ; Since the degree of the numerator is greater than the degree of the denominator. pg. 114. Correct answer is C.

f(x)=x³+lnx

f '(x)=3x²+1/x

f ''(x)=6x-(1/x)²

f '''(x)=6+2/x³

If demand is elastic, i.e. |E_p|>1, revenue R(p)=p q(p) decreases as price p increases.
If demand is inelastic, i.e. |E_p|<1, revenue R increases as price p increases.
If demand is of unit elasticity, i.e. |E_p|=1, revenue is unaffected by a small change in
price.

The market is in equilibrium when supply and demand are equal. So, equation these we find 10x-150=5x-100 from which we find x=10. Therefore, there will be market shortage when x<10.

1 ; limit of a constant is itself. pg. 107. Correct answer is B

(-1 – 1) (-1 – 1) = 4. pg. 110. Correct answer is E.