How do i solve this question

Mathematics

2 answers:

AfilCa [17]3 years ago

7 0

Mary spent 4/9 of her allowance on food and shopping. what fraction of her allowance had she left

KIM [24]3 years ago

3 0

Download an app called photomath, it will really help.tell me how it went after!

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Explain the error in the students work.

Usimov [2.4K]

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3 years ago

Consider the function below. (If an answer does not exist, enter DNE.) g(x) = 190 + 8x3 + x4 (a) Find the interval of increase.

galben [10]

Answer:

The interval of increase of g(x) is $(-6,+\infty)$ .

Step-by-step explanation:

The interval of increase occurs when first derivative of given function brings positive values. Let be $g(x) = 190 + 8 \cdot x^{3} + x^{4}$ , the first derivative of the function is:

$g'(x) = 24 \cdot x ^{2} + 4\cdot x^{3}$

$g'(x) = 4 \cdot x^{2}\cdot (6+x)$

The following condition must be met to define the interval of increase:

$4\cdot x^{2} \cdot (x+6) > 0$

The first term is always position due to the quadratic form, the second one is a first order polynomial and it is known that positive value is a product of two positive or negative values. Then, the second form must satisfy this:

$x + 6 > 0$