Astudy of driving costs based on 2012 medium-sized sedans found that the average cost (car payments, gas, insurance, upkeep, and depreciation) in cents per mile is approximately:

c(x) = 1910.5/x^1.72 + 42.9 (5 ≤ x ≤ 20)

where x (in thousands) denotes the number of miles the car is driven each year.

show that the graph of c is concave upward on the interval (5, 20).

Since the second derivative is positive for any value of the given interval then we can conclude that the graph of C is concave upwards on the interval (5, 20).

Step-by-step explanation:

We can find the second derivative of the function C(x) in order to determine its concavity.

To make the derivative process easier, we can begin rewriting it using negative exponents but no fractions using exponent properties.

Finding the first derivative.

We can work directly with derivative formulas and we get

Finding the second derivative.

Applying the derivative one more time we get

Writing it with positive exponents we get

Determining the concavity.

From the interval (5,20), we can pick any value and if we replace it on the second derivative, we will get a positive denominator, and since the numerator is also positive we can conclude that

Thus since the second derivative is positive on the interval (5, 20), then the graph of C is concave upward on such interval.

hey there!

if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

500 ÷ 6 =

she needs to save at least this amount each month, so we should use this symbol: ≥

let x be the amount she saves each month.

your final answer is x ≥

hope this !

step-by-step explanation:

the multiplicative inverse of a fraction a/b is b/a. for the multiplicative inverse of a real number, divide 1 by the number. for example, the reciprocal of 5 is one fifth 1/5 or 0.2, and the reciprocal of 0.25 is 1 divided by 0.25, or 4.