Question

Use the graph of f(x) = |(x2 − 4)(x2 + 2)| to find how many numbers in the interval [0, 1] satisfy the conclusion of the Mean Value Theorem.
None
1
2
3

Answer 1

Any ideas?

Answer 2

Well the domain of f(x) is continuous on the interval
[0,1]
But in that that interval
(x2-4) is negative

Answer 3

So what does that mean?

Answer 4

The equation of f(x) on that interval is
-(x2-4)(x2+)
Are the x suppose to be squared?

Answer 5

yes that is x squared where it says x2

Answer 6

So ur f(x) on the interval
[0,1]
f(x)=-(x^2-4)(2+x^2)
Now apply mean value theorem

Answer 7

i got [f(4) - f(1)] / (4 - 1)

Answer 8

does that seem right?

Answer 9

Quick question, have you already graphed the function?

Answer 10

yes

Answer 11

Yes that is the extreme value theorem

Answer 12

Yes that is the mean value theorem

Answer 13

so what does that mean in a case of an answer

Answer 14

1?

Answer 15

or 3?

Answer 16

Remember that the whole point of the mean value theorem is to find points on the graph where the tangent has the same slope as the average rate. The average rate can be found visually by drawing a line between (0,f(0)) and (1,f(1)). Then, look on the graph to see how many tangents between x = 0 and x = 1 have this same slope.

Answer 17

I claim that you can visually deduce that there are exactly 2 such points. See attached graph.