## Transcribed Text

TASK 1
Find the first derivative for the following functions:
f(x) = 1/3 x^4 - 2x^2 + 2
f(x) = (2x^2-1)/(1-x^3 )
f(x) = (x2 − ln x)5
f(x) = 1/2 x^3 e^5x
The population of a country is 13 million in 2019, and it is estimated that in the future it will grow by 1.15% annually.
i) Set up a function, P (t), which describes the evolution of the population over time. Let t = 0 correspond to 2019.
ii) How long will it take before the population is three times as high as in 2019?
Find the partial derivatives of 1st and 2nd order with respect to x and y of the following function:
f(x,y)= 1/3 xy^2− 3xy + 4y3
Let f (x) = ln (4x −1). Enter the definition quantity of the function and find f '(x) .
TASK 2
a) At the beginning of each year, $ 3000 is deposited into an account with annual interest and annual interest equal to 2.5%. How much is in the account just after the fifth deposit?
b) How long does it take for the balance to pass/exceed $ 25000 if $ 1500 is deposited
annually in an account with annual interest and annual interest equal to 3%?
c) We borrow $ 70000 at a monthly interest rate of 0.9%. The monthly installments are to be paid according to the annuity principle for a total of twelve installments, the first one month after borrowing. What will be the monthly installments?
TASK 3
Given f(x)= - 2/3 x^3 + 1/2 x^2+ 3x + 1
a) Find f '(x) and f ''(x).
b) Find the stationary points and determine if they are the top or bottom points.
c) Find any turning points.
d) Sketch the graph of f (x)
TASK 4
f(x,y) = 1/3 y^3 - 4xy + x^2 + 7y
Find any stationary points and classify them.

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