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masya89 [10]
2 years ago
13

To get to school each morning, Luis takes a scooter 12.97 kilometers and a car 5.63 kilometers. In total, the journey takes 51.4

7 minutes. How many kilometers is Luis's journey in total? kilometers
Mathematics
1 answer:
Crazy boy [7]2 years ago
4 0

He scoots 12.97 km and drives 5.63 km.

In total, the length of the journey is (12.97 + 5.63) = <em>18.6 kilometers</em>.

The time it takes him to cover the distance has no effect on the distance.


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ƒ(x) = x² - x – lnx

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Step 1. Find the zeros of the first derivative of the function

ƒ'(x) = 2x – 1 - 1/x = 0

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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

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ƒ'(x) < 0 so the function is decreasing on (0, 1).

(2) x = 2

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(b) Local extremum

ƒ(x) is decreasing when x < 1 and increasing when x >1.

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(c) Inflection point

(1) Set the second derivative equal to zero

ƒ''(x) = 2 + 2/x² = 0

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There is no inflection point.

(2). Concavity

Apply the second derivative test on either side of the extremum.

\begin{array}{lccc}\text{Test} & x < 1 & x = 1 & x > 1\\\text{Sign of f''} & + & 0 & +\\\text{Concavity} & \text{up} & &\text{up}\\\end{array}

The function is concave up on (0, ∞).

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