Graphing f(x)=x^2-x-ln(x)

Graphing f(x)=x^2-x-ln(x),

This problem is from Single Variable Calculus, by James Stewart,

blackpenredpen

calculus 1 derivative,
blackpenredpen calculus,
calculus tutorial,

[saschatrumper]

Since you are graphing the function and need the second derivative anyways:

if f'(x)=0 at x1 then look for f''(x1).. if f''(x1)>0, then the function f is concave up and you got a minimum. otherwise if f''(x1)<0, then f is concave down and you got a maximum. its easier that way, i think.

[omrimg]

Did you forget to edit this video or something? haha

[Ixion]

9:03 "so, let's save us some time" lmao

[ignorant-greg]

Love the uncut version, the signs are pure gold. It reminds me of when I try to explain things

[tonynguyen]

seeing this more than 3 years later and it still helps a lot. thank you!

[Arrrp]

Hi blackpenredpen, could you calculate by definition that the derivative of e^x is equal to e^x? Thanks in advance :)

[tfdtfdtfd]

for a complete graphing of this, you also need to find the asymptote at x->+oo

[mehrdadmohajer]

Hi bprp,
I approach it as summation of k(x) = (f(x) =x^2 )+( g(x)=-x ) - (l(x)=ln x), x>0

I just add : for y asymptote is left wings of the Graf much more shorter than shown. Point (1/e ; 0.76) is the touchdown f. Tangant to the asympttote.

[ufvoovy]

you 💓💓
I was confused with this problem 3hours to know the domain I search a lot to explain it until I find u😭😭😭😭😭💔💔💔

[omarifady]

7:20 9:17 Lol 😂 you are so funny ! Don’t delete it

[Wildlon]

Can I just take a moment to say how invaluable this channel's videos are to my interview prep for uni?

[seroujghazarian]

so g(x)=(2x^3-3x^2-6xlnx+6x)/6 has an inflection point at x=1, as both the first and the second derivatives are 0 at that point.

[JoseTorresNS]

Wooow thank you very much, I really liked the explanation

[dolev]

You should never edit your videos!
The uncut version is much more fun, isn't it?

[IITIAN_dost]

The range of f(x) is [1, infinity), am i right

[einsteingonzalez]

ln(x) is a transcendental function--that is, cannot be a solution to any polynomial with rational coefficients. Therefore, f(x)=x^2-x-ln(x) is a transcendental function!

[borg]

What software do you use to edit your videos?

[domanicmarcus]

How do we know (using Calculus) that the graph DOES NOT go below the x-axis? How did you know that the graph only touches that 1 point? Someone, please let me know