Question

determine where f(x) is increasing, f(x) = x^4, so wouldnt it just be increasing from where x gets to the 4th power?

Answer 1

@ittskathherine is this question from your calculus class?

Answer 2

It's not really from our textbook, but it's from this packet that my teacher gave us

Answer 3

but yes

Answer 4

Are you familiar with derivatives?

Answer 5

Not yet, we just started on the second day of school

Answer 6

While posting this question, i also found something that has to do with all real numbers in f(x), but idk how to find the interval on where it does increase.

Answer 7

This question, by its wording, is geared towards the use of derivatives which means that it would greatly help if you were familiar with them.

Basically, a function is increasing when the derivative of f(x), denoted as f'(x), is greater than 0, i.e. f'(x) > 0. Similarly, a function is decreasing when f'(x) < 0. You'll learn more as you go further in to the course.

Answer 8

But using what you know about functions and their graphs, we can still come to an educated conclusion as to where \(\bf f(x)=x^4\) is increasing even without the knowledge of derivatives. Firstly, we know that this is a monic polynomial (monic just means that the leading coefficient is 1) and the degree is 4 (even). This implies 2 things: firstly the function approaches infinity as x tends to negative or positive infinity and the function is even, i.e. \(\bf f(-x)=f(x)\). Let's examine the graph of this function:We note that it looks a lot like the graph of \(\bf f(x)=x^2\). We also note that the functions is increasnig (y-values get larger) when x is greater than 0, i.e. \(\bf f(x)\) is increasing for \(\bf x>0\).

Now we were able to deduce the interval of increase without much difficulty in this situation but that isn't always possible which is why derivatives are handy.

Answer 9

@ittskathherine

Answer 10

Thank you! But the derivatives, are they just f(x) <0 and f(x) > 0?

Answer 11

so is it increasing at (-infinity,0) U (0, infinity)?

Answer 12

Is that what you're saying?

Answer 13

It's only increasing on \(\bf x \in (0, \infty)\).

Answer 14

Which is the same as saying \(\bf x > 0\)..

Answer 15

OHHH okay, and that means it's decreasing at x in (-infinity, 0) right?

Answer 16

yup

Answer 17

THANK YOU SO MUCH!!

Answer 18

yw :)