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# Give an example of a function which has a derivative of 0 at x = 0 (not use a constant function)?

had this question on an online quiz, and had no idea what to put. this is the explanation it gave: "There are infinitely many solutions.

To give an example of a function that has a slope of 0 at x = 0, it's probably best to think about the graphs of some simple functions that might work -- remember that a slope of 0 means that your function should have a horizontal tangent at x = 0"

but I'm still confused, could someone give me a few examples or explain it differently? thanks

### 4 Answers

- MorningfoxLv 74 weeks ago
For a more complicated function, try this:

y' = 5x^4 + 4x^3+ 2x

Therefore,

y = x^5 + x^4 + x^2 + constant

- stanschimLv 74 weeks ago
f(x) = x^2, a parabola has a derivative equal to 0 at x = 0. Clearly, the slope of a tangent line at that point would be horizontal.

f(x) = cos(x) is another example.

- PuzzlingLv 74 weeks ago
How about something simple like this?

y = x²

It's a parabola with its vertex at (0,0). At the vertex of a parabola, the slope is zero.

Other answers that would work:

y = x² + 1

y = x^3

y = x^4 - 64

y = 2x^5

y = cos x