The extreme values of the function f(x) = x - 4sqrt(x) occur at the values of x for which f'(x) = 0
f'(x) = 1 - 2/sqrt(x) = 0
sqrt(x) - 2 = 0
sqrt(x) = 2
x = 4
To check for minimum or maximum,
f''(x) = 1/(sqrt(x))^3 = 1/(sqrt(4))^3 = 1/(2^3) = 1/8 => the point is a minimum.
Therefore, the minimum value = f(4) = 4 - 4sqrt(4) = 4 - 4(2) = 4 - 8 = -4 and occurs at x = 4.
Answer:
the theater needs to sell at least 100 tickets
Step-by-step explanation:
wants to make at least $1000 and they already have $50, so you take the $9.50 per ticket and add that to the $50.
$1000=$9.50t+$50
1000/50=9.5t
950=9.5t
950/9.5=t
t=100
Answer:
Angle N should be 64
Step-by-step explanation:
A triangle adds up to 180. So triangle JKL already has 60 towards 180. Triangle ONM already has 56 towards 180. So you have to find the other value needed in order to make 180. 56+60= 116 so we need to find the other angle to make 180. To do so just subtract 180-116 and that gives tou the answer 64 so that would be Angle N
Answer:
Option D
Step-by-step explanation:
Formula for the surface area of rectangular prism = 2(lb + bh + hl)
Here, l = Length of the prism
b = Width
h = Height
If l = 25 cm, b = 12 cm and h = 20 cm
Surface area of the rectangular prism = 2(25×12 + 12×20 + 20×25) cm²
Therefore, Option D will be the correct option.
Answer:
40%
Step-by-step explanation:
Let x = numerator
Let y = denominator
Decreased by 30% = 100% - 30% = 70% = 70/100 = 0.7
Decreased by 50% = 100% - 50% = 50% = 50/100 = 0.5
1.4 as a percentage = 1.4 x 100 = 140%
Therefore, the percentage increase is 140 - 100 = 40%
