chapter 9: Application of Differentiation

Presentation

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Mathematics

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12th Grade - University

•

Medium

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CCSS

HSG.GPE.B.5, HSA.CED.A.1, HSA.CED.A.4

Standards-aligned

Aziana Musa

Used 9+ times

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11 Slides • 9 Questions

Chapter 9: Application of Differentiation

9.1 Tangent and Normal

9.2 Extremum Problem

9.3 Application of Differentiation in Economics and business

9.1 Tangent and Normal Equation

$M_T=f'\left(x\right)=\frac{dy}{dx}$
$M_N=-\frac{1}{M_T}$
Equation $y-y_1=m\left(x-x_1\right)$

9.2 Extremum problems

$f'\left(x\right)=\frac{dy}{dx}=0$ to find stationary point(s)
2 method to find the nature of stationary points ( first derivative and second derivative)

Method 1 (First Derivative)

Method 2 (2nd Derivative/ f''(x))

$f''\left(x\right)>0\$ minimum point
$f''\left(x\right)<0$ maximum point
$f''\left(x\right)=0$ (test failed ) back to first derivative test)

Method 2 (second derivative)

9.3 Application of Differentiation in Economics and business

$\overline{C\left(x\right)}=\frac{C\left(x\right)}{x}$ (Average Cost)
$R\left(x\right)=p\left(x\right).x$
$\pi\left(x\right)=R\left(x\right)-C\left(x\right)$

Multiple Choice

Write the equation of the normal line of: $f\left(x\right)=2x^2-\frac{1}{x}$ at x = 1

$y=-\frac{1}{5}x+\frac{4}{5}$

$y=5x-6$

$y-1=5\left(x-1\right)$

$y-1=-\frac{1}{5}\left(x-1\right)$

Multiple Choice

What is the equation of the line tangent to f(x)= 4x²+2x-1 at x=0?

y+1=2(x+1)

y=2x-1

y=2x+2

y= -x-1

Multiple Choice

Local maximum point is obtained when

f ' (x) exchange from negative to positive

f '' (x) exchange from positive to negative

f ' (x) exchange from positive to negative

f '' (x) exchange from negative to positive

Multiple Choice

Which of the following is the equation for figuring out PROFIT?

Profit = Revenue - Cost

Profit = Cost - Revenue

Revenue = Profit - Cost

Costs = Profit - Revenue

Multiple Choice

Which of the following is the best definition of PROFIT?

The total amount of income a business makes from selling products or services

The amount of money a business has left over after paying for their costs.

The total amount of money a business spends.

Multiple Choice

What is the stationary points for the curve f(x) = x³ +3x² - 24x and determine their nature.

Maximum point : (2, -28) and minimum point : (-4, 80)

Minimum point : (2, 28) and maximum point : (-4, 80)

Minimum point : (2, -28) and maximum point : (4, 80)

Minimum point : (2, -28) and maximum point : (-4, 80)

Multiple Choice

What is the stationary point for the curve y=x²- 4?

A minimum at ( 0, -4)

A maximum at (0, -4)

A minimum at (0,4)

A maximum at (0,4)

Multiple Choice

If (a,b) is a local minimum, then what will be true about f'(a)?

It's positive

It's negative

It's zero

Cannot be determined

Multiple Choice

The revenue function for selling x kg of butter cake is given by

R\left(x\right)=30x-x^2.

the total cost to produce xkg of butter cake is given by the cost function

C\left(x\right)=10x+20

. Find the maximum profit

RM 100

RM 90

RM80

RM 120

Chapter 9: Application of Differentiation

9.1 Tangent and Normal

9.2 Extremum Problem

9.3 Application of Differentiation in Economics and business

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