# Differential Calculus (Math Problem Sample)

The students must be able to:

1) Use relevant mathematical tools, such as CAS and mathematical programs to solve given mathematical problems. Furthermore, use IT for calculations and examination of mathematical expressions

2) Recognize and switch between verbal, graphical, and symbolic representations of mathematical problem from the contents of the subject and evaluate in which cases the different presentation forms are appropriate

3) Complete simple mathematical reasoning and proofs

4) Handle formulas, e.g., translate from mathematical symbolic language to daily spoken and written text as well as use symbolic language to solve problem with a mathematical content

5) Read mathematical texts

6) Convey mathematical methods and results in an appropriate language

7) Master the minimum requirements of the subject

Differential Calculus 2

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Exercise 1

Part a

fx=4x4-3x2+2x-1

Using the derivative formula,

f'x=lim∆x→0fx+∆x-f(x)∆x

ddx(4x4-3x2+2x-1

Apllying the sum or diffrence rule:f±g'= f'±g'

ddx4x4=16x3

ddx3x2=6x

ddx2x=2

ddx1=0

Therefore,

=16x3-6x+2-0

=16x3-6x+2

The equation of the tangent to fxat x=3 will be

y=16x3-6x+2

= 1633-63+2

=416

Part b

Using the derivative formula,

g'x=lim∆x→0fx+∆x-f(x)∆x

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