At which points on the curve $ y = 1 + 40x^3 - 3x^5 $ does the tangent line have the largest slope?
Slope is maximum at $(2,225)$ and $(-2,-233)$
equals one plus 40 X cubed minus three X to the fifth. Does the tangent line have the largest? Look. Okay, so largest. We're gonna maximize something. Gonna maximize slope of the tangent line. All right? And to find the slope of the tangent line, we have to take the derivative. So m tan. Because why prime, which is 1 20 X square minus 15 x to the fourth. Okay, now, we're not gonna set that equal to zero because we're not looking for the tangent is equal to zero or looking for the maximum tangent. So we have to take the derivative of it in 10. Prime. So to 40 x minus 60 x cubed equals zero. We confected out of 60 x and we get four minus x squared. So X is plus or minus two. And so then why is one plus 40 times two cubed minus three times to to the fifth tomorrow. Plus too cute 40 minus 12 one. Plus, um, maybe why don't I just do this on my calculator? That might be easier. Okay, let's see now. You know what? I can do that to Cuba today. Eight times 43. 20 to do the 5th, 32 32 times 3 96. So 3. 21 minus 96 five two. So 2. 25. So two comma 2 25. And then if you put a minus in there, it's minus 3 28 plus 96. So it will be 3. 20 minus 97. So three forever tu minus 2 23 minus 2 a.m. minus 2. 23.