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3 years ago

Find the intervals on which the function is increasing or decreasing.

Mathematics

1 answer:

Assoli18 [71]3 years ago

6 0

To solve this, you have to know that the first derivative of a function is its slope. When an interval is increasing, it has a positive slope. Thus, we are trying to solve for when the first derivative of a function is positive/negative.

f(x)=2x^3+6x^2-18x+2
f'(x)=6x^2+12x-18
f'(x)=6(x^2+2x-3)
f'(x)=6(x+3)(x-1)
So the zeroes of f'(x) are at x=1, x=-3
Because there is no multiplicity, when the function passes a zero, he y value is changing signs.
Since f'(0)=-18, intervals -3<x<1 is decreasing(because -3<0<1)
Thus, every other portion of the graph is increasing.
Therefore, you get:

Increasing: (negative infinite, -3), (1, infinite)
Decreasing:(-3,1)

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3 years ago

If two distinct planes intersect , then their intersection is a line . Which geometry term does the statement represent

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Answer:

POSTULATE

Step-by-step explanation:

A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven

In geometry, the theorem is considered valid or correct with which its assertion is practically not refuted by almost anyone, whether it is really true or not.

This, in practice, implies that all students of the subject share the same criteria on the theory. Thus, the postulates, in short, have the following characteristics:

They are presumed true by most of the scholars in the field.

Its contradiction goes against the very essence of the subject.

Postulate 6: If two planes intersect, then their intersection is a line.

See Attachment for Details ^^

The image attached represents the statement given in the question (If two distinct planes intersect, then their intersection is a line)

Therefore,

The Geometry term that represents the statement above is POSTULATE

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3 years ago