RULES OF DERIVATIVES
FIRST & SECOND DERIVATIVE
CRITICAL POINTS
Optimization
MISCELLANEOUS
100
What is the derivative of: 10x^2-89x+sin(x)-9x(.3)
20x-89+cos(x)-2.7x^(-.7)
100
velocity represents what compared to the position function?
velocity is the rate of change of position, thus is the first derivative
100
find the critical points of: x^5- 10x^3 -8
0, +/- radical 6
100

The name for an equation that defines our limitations in an optimization problem.  For example, if we are trying to build the biggest pen out of 100ft of fencing, an equation like 100=2x+2y

constraint

100

What is the formula to use when conducting tangent line approximations?

L(x)= f(a) + f'(a) ( x-a)

200

what is the derivative of: tan(e^x)

sec^2(e^x)*e^x

200
acceleration represents what compared to the position function?
acceleration is the rate of change of velocity, or the derivative of the first derivative, thus it is the second derivative of the position function.
200

what are the critical points? 5x - 3

there are none

200

Every optimization problem is either looking for a ______ or a _______

max, min

200

On a certain interval, f'(x) < 0 and f''(x) > 0.  What must be true on the graph of f(x) based on this information?

decreasing and concave up

300

what is the derivative of: 12(x^3-2x)^6)

72(x^3-2x)^5

300
what is a critical point?
when the first derivative is equal to zero, the x-value found gives you your x value of your critical point
300
find the global max/ min extrema for the function on the closed interval: x^4- 8x^2 interval : -3
global min- x=+/- 2 global max- x=-3
300

A company is trying to making an ice cream cone that can hold 8 cubic inches of ice cream while using the least amount of cone material.  What geometric concept is our goal function (the quantity to be minimized)

surface area

300

Two correct answers required

 True or False: if a function is differentiable, it must be continuous. 

True or False: if a function is continuous it must be differentiable.

True- False

400

What is the derivative of: cos(sin(5x^3))

-sin(sin(5x^3))*cos(5x^3)*15x^2

400
what is an inflection point?
when the second derivative is equal to zero, or where there is a change in concavity.
400

The Mean Value Theorem can be summarized geometrically like this: On a smooth curve with a secant line drawn between two points, somewhere in between those points there is a tangent line that is ____________

parallel to the secant line

400

In an optimization problem, what should you do after rewriting the goal function in terms of a single variable?

take the derivative

400

What is the general antiderivative of f(x)=x^5?

(1/6)*x^6+C

500

What is the derivative of 1/(x^3)

-3/x^4

500

find all critical and inflection points: 6x-x^2

critical points: x= 3 inflection points: none

500

When a function has a positive derivative before a critical point, and a negative derivative after, what type of extremum must be found at the critical point?

local max

500

What numbers x and y satisfy the constraint x+y=10 and maximize the product, xy?

5 and 5

500

What is the general antiderivative of y=sin(x)+2cos(x)

-cos(x)+2sin(x)+C

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