Final Exam Review

Question 1

X—>2+, what does the + represent?

Answer 1

+ means from the Right

Question 2

X—>2-, what does the - represent?

Answer 2

• means from the Left

Question 3

If the right hand limit does not equal the left hand limit for f(x), it is said that the limit?

Answer 3

DNE or Does Not Exist

Question 4

The limit of f(x) exists if

Answer 4

RHL = LHL

Question 5

For limits, 1/big# =

Answer 5

0

Question 6

For limits, 1/tiny# =

Answer 6

Infty

Question 7

Difference Quotients Formula =

Answer 7

DQ = f(x+h)-f(x)/h

Question 8

Using limit definition, find the derivative for f(x)=2x^2+1 find slope of tangent line at x=2

Answer 8

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

Question 9

Find the EQUATION OF THE TANGENT LINE of f(x) = 2x^2+1 at x=2

Answer 9

Use slope intercept form y=mx+b or Point Slope Form Y-y1=m(X-x1)

y= 8x-7

Question 10

Find y’ for Y= -6√x

Answer 10

Y = -6x^1/2
y'= -3x^-1/2

Question 11

Find y’ for Y= 3/x - x/2

Answer 11

Y= 3x^-1 - 1/2x
Y' = -3x^-2 - 1/2

Question 12

^4√x^3 simplified is

Answer 12

x^-3/4

Question 13

y’ of e^4x =

Answer 13

e^4x X 4 X ln(e)

Question 14

f(x) = x^2015

f^(2017) =

Answer 14

0 because 2017 is higher than the original exponent 2015 TRICK QUESTION!

Question 15

Position Function =

Answer 15

s(t) which is given equation

Question 16

Velocity Function =

Answer 16

v(t) which is found after taking First Derivative from s(t)

Question 17

Acceleration Function =

Answer 17

a(t) which is found after taking Second Derivative from v(t)

Question 18

Product Rule =

Answer 18

f’(x) X g(x) + f(x) X g’(x)

Question 19

Quotient Rule =

Answer 19

f’(x) X g(x) - f(x) X g’(x) / g(x)^2

Question 20

Marginal Cost =

Answer 20

MC(X) = C’(x)

Question 21

P or Profit =

Answer 21

P = R-C

Question 22

Marginal Revenue =

Answer 22

MR(X) = R’(x)

Question 23

Marginal Profit

Answer 23

MP(X) = P’(x)

Question 24

How do you find Critical Values and Points of f(x) = 2x^3-3x^2-21x+12

Answer 24

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)