Taking Derivatives
Given y = 4x^3 - 1/2x^2 + 5x -10
find dy/dx
dy/dx=12x^2-x+5
How do you find a point of inflection?
Set f''(x)=0 and solve for x
Given the slope of m=-2 , find the normal (perpendicular) slope
m_|_=1/2
How do you find a critical point, maximum/minimum, or horizontal tangent?
Set f'(x)=0 and solve for x
What does Barteau say before every Skills Check and Exam?
"Good luck, do your best, and believe in yourself"
Given f(x)=sqrtx + 1/x^2
find f'(x)
f'(x)=1/2x^(-1/2)-2x^-3
or
f'(x)=1/(2sqrtx) - 2/x^3
Given y=x^3+x^2+x+67
find (d^2y)/dx^2
(d^2y)/dx^2=6x+2
Given f'(x)=x^2+x+2 , determine the slope at x=1/2
f'(1/2)=m=11/4 or 2.75
Given f(x)=x^2+4x use f'(x) to prove that the critical point at x=-2 is a minimum
f'(-3)=-2 meaning it is decreasing before x=-2 , and f'(-1)=2 which means it is increasing after x=-2
How many times can you retake a Skills Check?
Infinite
Given y=e^x x^2
find y'
y'=2xe^x+x^2e^x
or
y'=xe^x(2+x)
Given y=1/3x^3+3x^2
find the x-value of the point of inflection of y
x=-3
Find the equation of the tangent line to y=x^2 at x=2
y=4x-4
Given f(x)=x^3-4x^2-16x find the x-values of both critical points
x=4 and x=-4/3
How can you waive the late grade from any homework or practice packets?
Come to Office Hours to work on them
Given f(x)=(x+1)/x^2
find f'(x) in simplest form
f'(x)=(-x-2)/x^3
Given f(x)=1/5x^5
find f''(-1) AND describe its concavity at x=-1
f''(-1)=-4 so it is concave down
(like a frown)
Find the equation of the normal line to y=x^2 at the point (2,4)
y=-1/4x+4.5
Given a rectangle with width, w, height, h, and a total perimeter equal to 20, write an expression for h in terms of w
h=10-w
(go to 500 question)
What percentange of your grade is from:
1. Achievement (skills checks+tests)
2. Classwork (practice packets)
3. Preparation (homework)
1. Achievement - 70%
2. Classwork - 20%
3. Preparation - 10%
Given y=ln(4x^5)
find dy/dx in simplest form
dy/dx=5/x
Given y=1/6x^3-x^2 has a critical point at x=4 , use y'' to prove whether it is a maximum, minimum, or point of inflection
At x=4 , y''=2 . Therefore y is concave up and the critical point is a minimum.
Find the equation of the normal line to y=e^x at the x-value x=0
y=-x+1
Given the same rectangle with width, w, height, h, and a total perimeter equal to 20, we wrote that: h=10-w .
Write an expression for the area of the rectangle in terms of w , then find the value of w that maximizes area
w=5
What three things do you need to access a one-time Unit Exam retake?
1. All practice packets turned in
2. Exam corrections
3. "Ticket" practice question