Unit 6: Differential Calc
f(x) = 2x8 – 5x2 + 7
Find f'(x).
f'(x) = 16x7 – 10x
Find the integral using the reverse power rule.
∫(2x5 – 4x)dx
2x6/6 – 4x2/2 + C
Test scores are normally distributed with mean 78 and standard deviation 7. Find the probability of scoring under a 70.
.127
Which test requires you to enter data in the "Matrix" section of the calculator?
Chi-Squared Test of Independence
If h(x) = 3x2 – 8x, find h(4).
16
y = 1/2 x6 + 12x4 – 9x – 3
Find dy/dx.
dy/dx = 3x5 + 48x3 – 9
Calculate:
∫26 (x2 – 11)dx
25.3
Heights are normally distributed with a mean of 67 in and a standard deviation of 3 in. The shortest 20% of people are below what height?
64.5 in
You're performing a Chi-Squared GOF Test at a 5% significance level to see whether a certain data set follows a normal distribution. You get a p-value of 0.034. State your conclusion.
Reject H0. The data is NOT normally distributed.
Find the volume of a cone with height 20 and radius 4.
335
A company's profit is given by the equation P(x) = –2x2 + 500x, where x is the number of items sold.
How many items should they sell to maximize profit? (Hint: Find the derivative.)
125
Find the integral using the reverse power rule.
∫(5/x4)dx
5x–3/–3 + C
Heights are normally distributed with a mean of 67 in and a standard deviation of 3 in. The middle 30% of people are between what two heights?
65.8 and 68.2 in
A company claims its new toothpaste reduces the number of cavities people get. You perform a t-test to test this claim, using data from two groups:
Control group: 0 4 1 3 2 1 4
Test group: 1 0 2 1 3 0 0
State the null and alternative hypotheses.
Null: The mean number of cavities in each group is the same. (μ1 = μ2)
Alternative: The mean of the control group is greater than then mean of the test group. (μ1 > μ2)
Sam invests $2500 into an account with 4% interest, compounded quarterly. How much will she have in 10 years? (Round to the nearest dollar.)
$3722
y = 5x – 3/x6
Find dy/dx.
dy/dx = 5 + 18x–7
Estimate the area under the curve using the trapezoidal rule.
x 1 4 7 10 13
y 2 6 3 8 4
60
Test scores are normally distributed with mean 78 and standard deviation 7. If 200 students took the test, how many should score above a 90? (Round to the nearest whole number.)
9
Test grades for two classes are below. Test whether there is any difference in means between the two classes. State the p-value.
Class A: 80 55 70 95 60
Class B: 85 90 60 65 70
p = .834
John takes out a loan for $30,000 at a 3% interest rate, and pays it off in monthly installments. It takes 5 years to pay off the loan. How much was John's monthly loan payment? (Round to the nearest dollar.)
$539
Write an equation for the tangent line to the curve y = x2 – 4x + 2 at x=1.
(Hint: Slope, Point, Equation)
slope: -2
point: (1, -1)
y + 1 = –2(x – 1)
Let f'(x) = 3x2 + 2x. Given that f(1) = 10, find f(x).
f(x) = x3 + x2 + 8
100 students take an IQ test. You're doing a Chi-Square GOF Test to see whether the data follows a normal distribution with a mean of 100 and a standard deviation of 10. Calculate the "expected frequency" column.
Score Frequency
<85 8
85-95 22
95-105 40
105-115 19
>115 11
7
24
38
24
7
You have 100 Skittles with the following color distribution:
Red Orange Yellow Green Purple
17 32 21 20 10
Test whether the data follows a uniform distribution. State the p-value.
p = .0128
Find the surface area of a cone with radius 4 and slant height 7.
138