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# F(x)= X^4 - 8 using analytical methods

To find those values of x which the given function is increasing and those values of x for which it is decreasing

### 2 Answers by Expert Tutors

Mark M. | Math Tutor--High School/College levelsMath Tutor--High School/College levels
4.9 4.9 (821 lesson ratings) (821)
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f(x) = x4 - 8

f'(x) = 4x

f'(x) = 0 when x = 0

When x < 0, f'(x)  < 0, so f is decreasing

When x > 0, f'(x) > 0, so f is increasing

f(x) is decreasing on (-∞, 0) and is increasing on (0,∞).
Michael J. | Effective High School STEM Tutor & CUNY Math Peer LeaderEffective High School STEM Tutor & CUNY ...
5.0 5.0 (5 lesson ratings) (5)
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You can factor out F(x) using difference of perfect squares.

F(x) = (x2 - √8)(x2 + √8)

F(x) = (x - √8)(x + √8)(x2 + √8)

You only have 2 x-intercepts.  Therefore, the 4th degree function acts like a quadratic function.

Next, we find the vertex,  Since the formula for the x-coordinate of the vertex is  x=-b/2a,  the vertex is the point (0, -8).

Interval of decrease (-∞, 0)
Interval of increase (0, ∞)