Taking Derivatives
Given y = 4x^3 - 1/2x^2 + 5x -10
find dy/dx
dy/dx=12x^2-x+5
Given y=x^3+x^2+x+67
find (d^2y)/dx^2
(d^2y)/dx^2=6x+2
Find the equation of the tangent line to y=x^2 at the point (2,4)
y=4x-4
Given
y=-4x^2+16x find the full coordinates (x,y) of the critical point
(2,16)
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 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 tangent line to f(x)=ln(x) at the point (1,0)
y=x-1
Given f(x)=x^2+4x use f'(x) to prove that the critical point at (-2,-4) 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^3 at the x-value x=-1
y=3x+2
Given f(x)=1/3x^3+2x^2 find the x-values of both critical points
x=-4 and x=0
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)
f'(x)=(-x^2-2x)/x^3
or
f'(x)=(-x-2)/x^3
Given f''(x)=2x^2+x-3
find the x-value(s) of any points of inflection of y
x=-1.5 and x=1
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''=4 . 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