ch 3 Flashcards
extreme value theorem
if f(x) is continuous on a closed interval, then it has both a max and a min
rolle’s theorem
if f(x) is continuous on closed interval and differentiable on the open interval and the endpoints of the interval are equal, then there is a horizontal tangent line somewhere on the open interval
mean value theorem
if f(x) is continuous on the the closed interval and differentiable on the open interval, then somewhere on the open interval there is a tangent that equals the slope of the secant between the intervals
finding critical numbers
set f’(x) equal to zero
first derivative test
f’ changes from + to - it is a max and if from - to + it is a min
f is increasing when f’ is
> 0
f is decreasing when f’ is
<0
poi
points where f” = 0
f is concave down when
f”<0
f is concave up when
f”>0
2nd derivative test
f’(c) = 0 and f”(c)< 0 then c is a max and if f”>0 then c is a min
horizontal asymptote
line/number a graph approaches as x–> infinity or -infinity
linearization formula
y - f(c) = f’(c)(x-c)
will linearization be too big or too small?
if concave up then too small if concave down then too big
formula for actual change in y (delta y)
delta y = f(c+deltax) - f(c)
