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Challenge: Solving the Optimisation Problem | Mathematical Analysis
Mathematics for Data Analysis and Modeling

Course Content

Mathematics for Data Analysis and Modeling

## Mathematics for Data Analysis and Modeling

1. Basic Mathematical Concepts and Definitions
2. Linear Algebra
3. Mathematical Analysis

# Challenge: Solving the Optimisation Problem

Task

Let's consider a physics-related optimization problem where we need to find the maximum height reached by an object thrown vertically upward with a given initial velocity.

We have the following equation:
`h = v * t - 0.5 * g * t**2`
that describes the motion of an object.

Our task is to find the time `t` when the object reaches its maximum height and then find the maximum height `h_max`.

1. Calculate the derivatives of the first and second order for the `h` function.
2. Find critical points of `h` function.
3. Check if these critical points are points of the maximum of the function `h`.

Task

Let's consider a physics-related optimization problem where we need to find the maximum height reached by an object thrown vertically upward with a given initial velocity.

We have the following equation:
`h = v * t - 0.5 * g * t**2`
that describes the motion of an object.

Our task is to find the time `t` when the object reaches its maximum height and then find the maximum height `h_max`.

1. Calculate the derivatives of the first and second order for the `h` function.
2. Find critical points of `h` function.
3. Check if these critical points are points of the maximum of the function `h`.

Everything was clear?

Section 3. Chapter 5

# Challenge: Solving the Optimisation Problem

Task

Let's consider a physics-related optimization problem where we need to find the maximum height reached by an object thrown vertically upward with a given initial velocity.

We have the following equation:
`h = v * t - 0.5 * g * t**2`
that describes the motion of an object.

Our task is to find the time `t` when the object reaches its maximum height and then find the maximum height `h_max`.

1. Calculate the derivatives of the first and second order for the `h` function.
2. Find critical points of `h` function.
3. Check if these critical points are points of the maximum of the function `h`.

Task

Let's consider a physics-related optimization problem where we need to find the maximum height reached by an object thrown vertically upward with a given initial velocity.

We have the following equation:
`h = v * t - 0.5 * g * t**2`
that describes the motion of an object.

Our task is to find the time `t` when the object reaches its maximum height and then find the maximum height `h_max`.

1. Calculate the derivatives of the first and second order for the `h` function.
2. Find critical points of `h` function.
3. Check if these critical points are points of the maximum of the function `h`.

Everything was clear?

Section 3. Chapter 5

# Challenge: Solving the Optimisation Problem

Task

Let's consider a physics-related optimization problem where we need to find the maximum height reached by an object thrown vertically upward with a given initial velocity.

We have the following equation:
`h = v * t - 0.5 * g * t**2`
that describes the motion of an object.

Our task is to find the time `t` when the object reaches its maximum height and then find the maximum height `h_max`.

1. Calculate the derivatives of the first and second order for the `h` function.
2. Find critical points of `h` function.
3. Check if these critical points are points of the maximum of the function `h`.

Task

Let's consider a physics-related optimization problem where we need to find the maximum height reached by an object thrown vertically upward with a given initial velocity.

We have the following equation:
`h = v * t - 0.5 * g * t**2`
that describes the motion of an object.

Our task is to find the time `t` when the object reaches its maximum height and then find the maximum height `h_max`.

1. Calculate the derivatives of the first and second order for the `h` function.
2. Find critical points of `h` function.
3. Check if these critical points are points of the maximum of the function `h`.

Everything was clear?

Task

Let's consider a physics-related optimization problem where we need to find the maximum height reached by an object thrown vertically upward with a given initial velocity.

We have the following equation:
`h = v * t - 0.5 * g * t**2`
that describes the motion of an object.

Our task is to find the time `t` when the object reaches its maximum height and then find the maximum height `h_max`.

1. Calculate the derivatives of the first and second order for the `h` function.
2. Find critical points of `h` function.
3. Check if these critical points are points of the maximum of the function `h`.

Section 3. Chapter 5
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