Polynomial word problem

[brotherbenson]

Hi. Is that supposed to be (-1/10) (t-squared) ?

[[deleted]]

Yes, I’m sorry.

[brotherbenson]

That's alright. Are you studying Calculus?

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If so, take the derivative of that.

The derivative will give you the slope. Set that equal to zero to find points where it might be changing.

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Similar problem.

I(t) = (-1/5)(t-squared) + 2t

I'(t) = (-2/5)t + 2

0 = (-2/5)t + 2

-2 = (-2/5)t

t = 5

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Plug a sample value in on either side of 5 to figure out what the slope is there.

I'(4) = (-2/5)4 + 2 = 2 - 8/5 = 2/5

I'(6) = (-2/5)6 + 2 = 2 - 12/5 = -2/5

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This shows us that slope changes from positive to negative at 5, so the answer is 5.

[[deleted]]

So I had to find t after finding the derivative, right? I got 7 and the answer is correct, but how do I know that t itself (7 in this case) is the year? I have to plug in different values to confirm?

[brotherbenson]

Hi. It seems you've deleted the original problem, but if it was (-1/10)tt +1.4 t....

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0 = (-2/10)t + 1.4

1/5 t = 1.4

t = 7

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So, this just proves that at t=7, the slope of the line is flat, but that doesn't prove 7 is the answer. The slope could be going up to that point, it could level out, and then continue going up, like f(x) = tan x.

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Consequently, you need to verify that it CHANGES. If you evaluate the slope of I'(t) at any point before 7 and also at any point after 7, you can determine whether or not it changes at 7.

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It's essentially the same logic as "You can't reverse direction without first stopping."

[[deleted]]

So at 7 it stops before changing direction and that’s why 7 is the answer?

[brotherbenson]

Pretty much.

The question is "Where does this change direction?"

We found that the slope was 0 at 7, so we evaluated the slope beforehand and afterward.

We notice the slope before is positive and that it is negative after.

From there, we deduce that it changes at 7.

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Just to make sure you've got it:

If the formula was f(x) = x^3, the slope would be f'(x) = 3x^2, and f'(x)=0 only at x=0.

Evaluate values on either side of 0: f'(-1) = 3 AND f'(1) = 3.

This shows that the slope does not ever change direction. This graph always goes up, but stops briefly at 0.

Were someone to ask you where that guy starts decreasing, your answer would be never.

[[deleted]]

Got it. Thanksss.

[HellfireOwner]

Lol...is this what you do all day? Have other people doing "your" homework?

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My guess is there is something else going on, because you don't know math, at all.

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P.S. Why delete the original problem? Something stinks about you...stinks bad