Number 8 please help 10 points no links pleAse
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:
x = -
Step-by-step explanation:
Given
(x + 5
) =
Multiply both sides by 8 to clear the fractions
6(x + 5 ) = 5 ← distribute parenthesis on left side
6x + 33 = 5 ( subtract 33 from both sides )
6x = - 28 ( divide both sides by 6 )
x = = -
She need 1/12 cup of oil. A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters.
<h3>What is meant by fraction?</h3>- A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters.
- fraction, A number expressed as a quotient in arithmetic, in which a numerator is divided by a denominator. Both are integers in a simple fraction.
- A complex fraction contains a fraction in either the numerator or the denominator. A proper fraction has a numerator that is less than the denominator. A fraction is a portion of a whole number and a method of dividing a number into equal parts.
- She needs 1/3 cup of oil
- She have 1/4 cup of oil
To find how much need to obtain 1/3 of cup
we need to subtract what we have from what we need.
so , we have 1/4 and need 1/3
= 1/3 - 1/4
=
= 1/12
she need 1/12 cup of oil more to make cake.
To Learn more about fraction refer :
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