Final Exam Review Flashcards
X—>2+, what does the + represent?
+ means from the Right
X—>2-, what does the - represent?
- means from the Left
If the right hand limit does not equal the left hand limit for f(x), it is said that the limit?
DNE or Does Not Exist
The limit of f(x) exists if
RHL = LHL
For limits, 1/big# =
0
For limits, 1/tiny# =
Infty
Difference Quotients Formula =
DQ = f(x+h)-f(x)/h
Using limit definition, find the derivative for f(x)=2x^2+1 find slope of tangent line at x=2
lim h->0 = f(x+h)-f(x)/h
2(x+h)^2 +1 - (2x^2+1)/h
then solve and f’(x)= 4x
plug in for slope of target 4(2) = 8
Find the EQUATION OF THE TANGENT LINE of f(x) = 2x^2+1 at x=2
Use slope intercept form y=mx+b or Point Slope Form Y-y1=m(X-x1)
y= 8x-7
Find y’ for Y= -6√x
Y = -6x^1/2 y'= -3x^-1/2
Find y’ for Y= 3/x - x/2
Y= 3x^-1 - 1/2x Y' = -3x^-2 - 1/2
^4√x^3 simplified is
x^-3/4
y’ of e^4x =
e^4x X 4 X ln(e)
f(x) = x^2015
f^(2017) =
0 because 2017 is higher than the original exponent 2015 TRICK QUESTION!
Position Function =
s(t) which is given equation
Velocity Function =
v(t) which is found after taking First Derivative from s(t)
Acceleration Function =
a(t) which is found after taking Second Derivative from v(t)
Product Rule =
f’(x) X g(x) + f(x) X g’(x)
Quotient Rule =
f’(x) X g(x) - f(x) X g’(x) / g(x)^2
Marginal Cost =
MC(X) = C’(x)
P or Profit =
P = R-C
Marginal Revenue =
MR(X) = R’(x)
Marginal Profit
MP(X) = P’(x)
How do you find Critical Values and Points of f(x) = 2x^3-3x^2-21x+12
TAKE FIRST DERIVATIVE
f’(x) = 6x^2=6x-12 = 0 (set equal to zero)
x^2-x-2 = 0
(x-2)(x+1) = 0
X=2 x=-1 are the critical values plug back into original equation to find CRITICAL POINTS (x,y) , (x,y)
