Mean Values
Extreme Values
Extreme Values (visual)
Surprise!!
100
F'(c)=[f(b)-f(a)]/b-a
Mean Values Theorem
100
Can I have a hole be my max?
No, because I have no actual point there.
100
(3,-10)
The universal min and end point?
100
I can't find a derivative at?
A hole, a jump/discontinuity, where it goes to infinity, vertical tangent.
200
What do I have to test for in order to know if the MVT will work?
1. f(x) has to be continuous [a, b]
2. f(x) has to be differentiable (a, b)
200
Does y=x2 -5x+7 has a absolute max? A min?
Max= no
Min=yes
200
(2, 16)
Local man
200
Find f(x) if:
f'(x)=4x3
f(x)=x4
300
Can I use the MVT on this equation?
y=(x-2)/(x+4)2 over the interval [-10, 10]
No, we have a domain issue. An azymptote.
300
Find the critical points for y=x3+3x2-2
(-2,2) and (0,-2)
300
A= B= C= D= E= F=
A, C, E= local max
B, D, F= local min
A= universal max
F= universal min
300
Apply the MVT on y=(x2+10x+25)/(x2-5) over the interval [-8, 6]
The MVT does not work over this interval, we have a hole and a asymptote.
400
Find where the ARC equal the SRC:
y=x2 on [0, 2]
(1, 1)
400
Find the absolute max and absolute min of y=x3-6x2+pi on the interval [-3, 5]
Max= 3.14
Min=-77.85
400
Find dy/dx
y=esin^2(4x^3)
=esin^2(4x^3) 2sin(4x3) cos(4x3) 12x2