Derivative Rules
Find the First derivative of y=9√x
Explain what rules you used to get the answer
9/2 x-1/2
What is a critical point?
What is an inflection point?
critical point - when the first derivative is 0
Inflection point - when the second derivative is 0
Identify the global and local max and mins in the graph I will draw on the board.
TBD :)
Marginal revenue is really finding what?
The first derivative / slope
What is the derivative of ax
What is the derivative of ex
What is the derivative of ln(x)
ln(a) x ax
ex
1/x
find the first derivative of
t= z3+ 4/z2 + 6z-3
Explain what rules you used to get the answer
3z2 - 8z-3 - 18z-4
Explain the first and second derivative tests. Which should you use first and why?
1st derivative test: if the first derivative changes from negative to positive, then F has a local minimum. if the first derivative changes from positive to negative, then f has a local maximum.
2nd derivative: plug the critical points into the second derivative and observe the behavior.
second derivative first because its quicker. if you get 0 as an answer, it tells you nothing about the function and you then have to try the first derivative test.
Identify the steps in finding global max and min
1. identify if it is on a closed or open interval
2. find the first derivative
3. evaluate at the endpoints (if present) and critical points
4. if open interval, classify critical points and sketch
5. determine max and min
a manufactoring company has a cost function c(q)=3000+20q and a revenue function of
R(q) = - q2+1000q
find the quantity that maximized profit
what is that profit?
q = 490
Profit = 237,100
given f(x) = e-x + x , find the derivative
-e-x + 1
Explain the chain rule in your own words
plug the inside function into the derivative of the outside function
Multiply that by the derivative of the inside funciton
Find all of the critical points of f(x)= 2x3 + 9x2 + 12x. Identify critical points as local maximum, minimum, or neither. Find any inflection points.
-2 = local max
-1 = local min
-1.5 = inflection point
f(x) = x3 - 3x2 - 9x +15
determine global and local max and mins
-1 = global max
3 = local min
-5 = global min
-140 = global min
TRIVIA !!!
Forward, I am heavy; backward, I am not. What am I?
TON
Find the derivative of y= t2 ln(t)
2tln(t) + t2/t
W(s) = 6e√s
3e√s (s-1/2)
Find all critical points and inflection points. classify each as a local max, min, or neither.
CP = -3, 2
IP = -12
-3 = local max
2 = local min
find the exact global max and min
g(x) = 4x-x2-5
x= 2, global max
Revenue is given by r(q)=450g and cost is given by c(q)=10,000+3q2 at what quantity is profit maximized? what is the total profit at this production?
Max profit occurs at q=75
the total profit will be $6875
find the equation of the tangent line
y= (2x+4)2 at x=1
y=-8x + 12
Find the derivative of f(t) = 5t e5-2t
5e5-2t - 10e5-2t
Find the critical points and identify the local max and min for f(x)=x3-9x2-48x+52
CP = -2, local max
CP = 8, local min
Find the exact global max and min
g(t) = te-t for t>0
No solution
A water park finds that with an admission price of $12, attendance is 400 per day. For every $1 decrease in price, 40 more people visit the park per day. What is the park attendance when admission prices are set to maximize revenue (to the nearest person)?
$11
find the equation the line tangent to f(x)=7xlnx at the point where x=1
y=7x-7