Question

absolute maximum and minimum for 5x^2-6x+5 on interval [0,5]

Answer 1

What part are you getting stuck on Jose?

We can find max/min points when \(\large f'(x)=0\). Solving for x will get us the max/min points that we need.

Have you taken the derivative of the function?

Answer 2

Since it's a closed interval, I guess we'll also have to check the end points. We'll deal with that after the derivative portion though :)

Answer 3

yes i have derivative is 10x-6 and i got x=6/10
i do not know where to go from here

Answer 4

So we found 1 critical point.
So we'll have three total points to check.

The critical point that we found, and the boundary values.
We'll plug each of these into the `original` function, and see which gives us the largest output, and which the smallest.

It's as simple as that!

Answer 5

\[\large f(x)=5x^2-6x+5\]

\[\large f\left(\frac{6}{10}\right)=?\]\[\large f(0)=?\]\[\large f(5)=?\]

Answer 6

F(6/10)=23/10
f(0)=5
f(5)=100

Answer 7

Hmm so it looks like x=6/10 gave you the smallest value ~ your minimum.
And x=5 gave you the largest ~ your maximum.

It's probably good to write your answer in ordered pair notation.
\(\large min=(6/10,\quad 23/10)\)
\(\large max=(5,\quad 100)\)

Answer 8

yea that was what I had thought, it was because this online site for my homework asked for values so i had been putting in x values, yet wen i put solely the y value it accepted the answer. thanks for your help.

Answer 9

cool c: