Caleb bought groceries and paid $1.60 in sales tax the sales tax rate is 2.5% what was the price of Caleb's groceries before tax
1 answer:
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Answer:
(a) Decreasing on (0, 1) and increasing on (1, ∞)
(b) Local minimum at (1, 0)
(c) No inflection point; concave up on (0, ∞)
Step-by-step explanation:
ƒ(x) = x² - x – lnx
(a) Intervals in which ƒ(x) is increasing and decreasing.
Step 1. Find the zeros of the first derivative of the function
ƒ'(x) = 2x – 1 - 1/x = 0
2x² - x -1 = 0
( x - 1) (2x + 1) = 0
x = 1 or x = -½
We reject the negative root, because the argument of lnx cannot be negative.
There is one zero at (1, 0). This is your critical point.
Step 2. Apply the first derivative test.
Test all intervals to the left and to the right of the critical value to determine if the derivative is positive or negative.
(1) x = ½
ƒ'(½) = 2(½) - 1 - 1/(½) = 1 - 1 - 2 = -1
ƒ'(x) < 0 so the function is decreasing on (0, 1).
(2) x = 2
ƒ'(0) = 2(2) -1 – 1/2 = 4 - 1 – ½ = ⁵/₂
ƒ'(x) > 0 so the function is increasing on (1, ∞).
(b) Local extremum
ƒ(x) is decreasing when x < 1 and increasing when x >1.
Thus, (1, 0) is a local minimum, and ƒ(x) = 0 when x = 1.
(c) Inflection point
(1) Set the second derivative equal to zero
ƒ''(x) = 2 + 2/x² = 0
x² + 2 = 0
x² = -2
There is no inflection point.
(2). Concavity
Apply the second derivative test on either side of the extremum.
The function is concave up on (0, ∞).
Answer:
Edward drove altogether of 16.1 miles.
Step-by-step explanation:
Given:
Edward was Running around on his bike.
Distance from home to post office =
can be Rewritten as
Distance from home to post office =
Now Given:
Distance from Post office to market = 3.25 miles.
Now we will calculate Distance from Home to market.
Distance from Home to market can be calculated by adding Distance from home to post office and Distance from Post office to market.
Framing in equation form we get;
Distance from Home to market =
Also Given:
his mother picked him up at the market and drove him home.
We need to find the total miles Edward drive altogether.
total miles Edward drive altogether will be equal to Sum of Distance from Home to market and Distance from market to home.
framing in equation form we get;
Total Distance Edward drove =
Hence Edward drove altogether of 16.1 miles.