Speed Trig
sin(𝜋/6)
1/2
Use the 1st derivative rule to find all extrema of the following:
y= 2x4-4x2+1
Local mins at (-1,-1) (1,-1)
Local max at (0,1)
Determine the exact value without using a calculator:
log3(81)
4
Find the derivative (y')
y=2x3-4x
y'=6x2-4
Find the mean of the following data set: {22.3,25,31.5,33,20,19.2,40}
27.286
tan(3𝜋/4)
-1
Use the 2nd derivative rule to find the x coordinate of the point of inflection:
y=4x3+21x2+36x-30
x=-7/4
Simplify the following into one logarithmic expression:
log(3)+4log(x)−7log(y)
log(3x4y-7)
Find the derivative f'(x):
f(x)=(3x2)(4x)-x1/2
36x2-(1/2)x-1/2
Find the median of the following data set: {12,13,22,22,14,6,33,25,25,19}
20.5
sec(4𝜋/3)
-2
Using the 2nd derivative test for extrema, find the local extreme values of:
f(x)=x3-12x-5
local mins at (2,-21)
9(x-4)(x+3)=815x
x=-1
x=12
Find the derivative dy/dx:
y=2x3/x2
2
Find the IQR of the following data set: {5,8,3,9,20,13,14,12,55}
10.5
cot(11𝜋/6)
-√3
Find all extrema:
y=x3+3x2-2
min at (0,-2)
max at (-2,2)
Write the following as a single logarithmic expression:
ln(x)+(1/2)[ln(y2+z2)]
ln(x√y2+z2)
Find df/dx if:
f(x)=(x2-7x)-3
-3(x2-7x)-4(2x-7)
A student scored 75 on a history test, where the average score was 80 and the standard deviation was 6. What is the z-score for this student's test?
-0.83
arctan(√3)
𝜋/3
find the x coordinates of all extrema:
y=3x5-25x3+60x+20
x= -2, -1, 1, 2
Use the change of bass formula to evaluate the following:
log(2/3)(53)
−9.792
Find dy/dx:
y=sin(x/3)tan(x2)
(1/3)cos(x/3)tan(x2)+sin(x/3)(2xsec2(x2))
An Uber driver earns an average of $65 per morning, with a standard deviation of $9. One morning, they earned $99. Calculate the z-score for the driver's earnings on that day.
3.78