The value of the derivative at the maximum or minimum for a continuous function must be zero.
<h3>What happens with the derivative at the maximum of minimum?</h3>
So, remember that the derivative at a given value gives the slope of a tangent line to the curve at that point.
Now, also remember that maximums or minimums are points where the behavior of the curve changes (it stops going up and starts going down or things like that).
If you draw the tangent line to these points, you will see that you end with horizontal lines. And the slope of a horizontal line is zero.
So we conclude that the value of the derivative at the maximum or minimum for a continuous function must be zero.
If you want to learn more about maximums and minimums, you can read:
brainly.com/question/24701109
Answer:
x= first number y= second
x=2y+9 and x+y=129, these are the equations...solving gives x=89,y=40
Step-by-step explanation:
Answer:
Samuel slept for 1/4 of the distance.
Step-by-step explanation:
The information provided are:
- Samuel fell asleep halfway home.
- He didn't wake up until he still had half as far to go as he had already
- gone while asleep.
Consider that the total distance covered was 1.
Then from the first point we know that Samuel fell asleep after covering a distance of 1/2.
It is provided that he woke up only after covering half of the remaining distance.
That is, he slept for 1/4 of the remaining distance.
Thus, Samuel was asleep for 1/4th of the entire trip home.
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I think the answer would be D. Hope this helps!