Confused about trapezoid rule

Question

legomyego180 · Answer

So Im watching this youtube video to help me solve a problem, and the lecturer chooses her max value to plug into the second derivative to be 1 at about the 2:50 mark. Clearly 1 cant be the max right?

legomyego180 · Answer

Video in question: https://www.youtube.com/watch?v=IbNHFt8uq_U

legomyego180 · Answer

my point being for

$$f(x)=\int\limits_{1}^{3}\sqrt{x}$$

$$f(1) \le f(4)$$

So the max would need to be 4, not 1 right?

jim_thompson5910 · Answer

1 is the smallest value of the interval [a,b] = [1,3]

the smallest value of x leads to the denominator being the smallest possible, which means the overall fraction itself is maxed out

legomyego180 · Answer

so is the point to take the max of the second derivative and not the function?

zepdrix · Answer

@legomyego180 where is this 4 coming from?

jim_thompson5910 · Answer

the second derivative is a function of its own

but yes, the point is to max out f '' (x) to find k

legomyego180 · Answer

sorry, my homework has the same problem but the bounds are 1 to 4. I mean 3.

jim_thompson5910 · Answer

sorry |f '' (x)|

legomyego180 · Answer

Got it, that is the case every time right? Just to make sure. Find the second derivative of the original function, then determine the maximum of the second derivative function?

jim_thompson5910 · Answer

a graph will help show this https://www.desmos.com/calculator/n2nejq4c26

jim_thompson5910 · Answer

`Just to make sure. Find the second derivative of the original function, then determine the maximum of the second derivative function?`
yes that will yield k

legomyego180 · Answer

Awesome, thank you jim and zep.

jim_thompson5910 · Answer

no problem