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Gnesinka [82]
2 years ago
9

Let f(x) = (1 − x2)2/3. Which type of non-differentiable point exists at x = 1?.

Mathematics
1 answer:
slava [35]2 years ago
3 0

f(x)=(1-x^2)^{\frac{2}{3}}\implies \cfrac{df}{dx}=\cfrac{2}{3}(1-x^2)^{-\frac{1}{3}}\implies \cfrac{df}{dx}=\cfrac{2}{3\sqrt[3]{1-x^2}}

when it comes to a rational expression, we can get critical points from, zeroing the derivative "and" from zeroing the denominator alone, however the denominator provides critical valid points that are either "asymptotic" or "cuspics", namely that the function is not differentiable or not a "smooth line" at such spot.

if we get the critical points from the denominator on this one, we get x = ±1, both of which are cuspics.  Check the picture below.

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kakasveta [241]

Answer:

roots : 4, -4, i, -i

Step-by-step explanation:

This gets a bit tricky.

We have to substitude x^2 as u in this problem.

Now to rewrite x^4 − 15x^2 − 16 = 0 with u, we get

u^2 - 15u - 16 = 0

( u - 16) (u + 1)

U = 16

U = -1

<em>This is not the end of the problem. </em>

Now we have to substitute x^2 back to u.

x^2 = 16  --> we get the roots 4 and -4

x^2 = -1 --> we get the roots i and -i

tadah!

8 0
2 years ago
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KonstantinChe [14]

Answer:

<u>8</u>

Step-by-step explanation:

The given monomial is :

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<u />

The degree of the monomial is the highest power to which a variable is raised to in the monomial. The greatest power in this case belongs to b⁸, which has a power of 8.

Hence, the degree of the monomial is <u>8</u>

5 0
2 years ago
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Natalka [10]

Answer: 3x^4 +x^3 -2x^2 +3x +2

Step-by-step explanation:

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There are no like terms for 3x^4, so leave it alone.

-2x^3 + 3x^3 = 1x^3

No like terms for -2x^2

4x - x = 3x

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Answer? 3x^4 +x^3 -2x^2 +3x +2

(Please mark brainliest! :) )

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Step-by-step explanation:

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3 years ago
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