Help please! Can someone show me how to do this?
If f(x) = ∣(x^2 − 6)(x^2 + 2)∣, how many numbers in the interval 1 ≤ x ≤ 2 satisfy the conclusion of the mean value theorem?

Question

Help please! Can someone show me how to do this?
If f(x) = ∣(x^2 − 6)(x^2 + 2)∣, how many numbers in the interval 1 ≤ x ≤ 2 satisfy the conclusion of the mean value theorem?

kaleidoscopicsink · Answer

@zepdrix

dinamix · Answer

the number in  this interval is 12 13 14 15 this 4 numbers

dinamix · Answer

calcul f(1) and f(2) that's only

kaleidoscopicsink · Answer

What?

mathmale · Answer

Kaled:  I'd suggest we go thru the calculus necessary to answer this question.
First of all, multiply out the two factors of f(x), and tehen find the derivative of the result.  Alternatively, use the Product Rule for Differentiation to find the derivative of f(x) without first multiplying out the two given factors.  Your turn.

kaleidoscopicsink · Answer

Okay, so the multiplied factor is |x^4 - 4x^2 - 12| then its derivative is | 4x^3 - 8x|?
@mathmale

mathmale · Answer

I'm not going to check the algebra, but rather take your word for it.  

Next, could you pleasae look up the "Mean Value Theorem"?     There are certain conditions that must be met for the conclusion of the Theorem to be true.  What are they?

And what equation represents that conclusion?

kaleidoscopicsink · Answer

$$f'(c)=\frac{ f(b)-f(a) }{ b-a }$$

triciaal · Answer

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