concepts
Limits
derivatives
Derivatives
2
2
Etc. ;3c
100
what is this?
f(x) = xk
f'(x) = kxk-1
power rule
100
Find the limit as x goes to 3 of 2x+6
12
100
Find d/dx
x2+6
2x
100
Find d/dx
y= (x2+1)5
10x(x2+1)4
100
For y= 2x2=1
find the average rate of change as x changes from 1 to 3
7
200
What is this?
f'g + g'f
product rule
200
Find the limit as h goes to -2 of 4h2-12.
4
200
Find d/dx
4x2+x-6
8x+1
200
Find the derivative
(x-5)(x+3)
f'(x)= 2x-2
200
A non-descript population/ total variable cost, in thousands, can be modeled by the function
P(t)= 1.1(1.0313)t
where t is the number of years since 2009. What will the population/price be in 2024?
1.75 thousand by 2024
300
What is this?
(fg' - gf')/g2
quotient rule
300
Find the limit as x goes to 5 of (x2-3x-18)/(x-6)
8
300
Find d/dx (simplify your expression so all the exponents are positive)
x-4 - 9x-3 + 8x-2 + 12
(-4/x5) + (27/x4) - (16/x3)
300
find the d/dx
(2x-5)2
y'=4(2x-5)
300
find the difference quotient for
y= 4/x
DQ= (4/x+h)-(4/x)/h
400
what is this?
d2y/dx2
second derivative
400
Is f continues at x = 1?
x - 2 x<1
f(x) = x2 + 1 1<=x<3
5/x 3<=x
Since left side = -1 and right side = 2 so DNE
400
Find d/dx
x1/2 + 8x2/3 - 2(x)1/4
1/(2(2)1/2) + 8/(3(x)2/3) - 1/(2(x)3/4)
400
find the derivative of
y=(x3+2)3(x2-1)4
y'= [9x2(x3+2)2(x2-1)4]+[8x(x2-1)3(x3+2)3]
400
Find the equation of the line tangent to the graph of f(x) = -5x3 - 3x2 + x + 3 at x=1
y = -20x+16
500
what is this?
f ' (x) = lim h→0 [ f(x + h) - f(x) ] / h.
derivative quotient/
difference quotient/
limit quotient
500
Find limit as x goes to 0 of x/((2+3x)1/2-(2)1/2)
(2(21/2))/3
500
Find d/dx
10(x3/5)-x7/2+6(x8/3)-3+ex
(6/(x)2/5)-(7(x)5/2/2)+16x5/3+ex
500
find the derivative of
((4x+5)/(3x-2))^-3
-69/(3x-2)^2((4x+5)/(3x-2))^-3
500
Is this a function? why or why not?
No, it fails the vertical line test