# Calc Final Exam Review Part Chp4

version from 2015-12-09 19:27

## Section

Fermat's TheoremIf f (c) is a local extrema and f is differentiable, then f ′(c) = 0.
Mean Value TheoremIf f is differentiable and continuous on [a, b], then there exists c in [a, b] where, f'(c)=(f(b)-f(a))/(b-a)
If f(x) is not continuous f(x) can still have extreme values
If f(x) is continuous but has no critical numbers on [a,b]Then either f(a) or f(b) is the absolute minimum value
If f has a secant line of slope 0Then f has a tangent line of slope 0
Local extrema occur where?at critical points
For a differentiable function on an interval... There always exists a point whose instantaneous rate of change equals the average rate of change.
Steps for solving related rates1) Draw a diagram and define the variables. 2) Find an equation relating those variables 3) Differentiate both sides of the equation from Step 2 with respect to t 4) solve for the unknown quantity
RectangleA=L•W, P=2L + 2W
CircleArea=πr^2 Circumference=2πr
SphereSA=4πr^2, V=4/3πr^3
CylinderSA=2πr^2+2πrh, V=πr^2h
ConeSA=πrh, V=π/3r^2h
CubeSA=6s^2, V=s^3