Course Content

Mathematics for Data Analysis and Modeling

## Mathematics for Data Analysis and Modeling

# 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`

.

- Calculate the derivatives of the first and second order for the
`h`

function. - Find critical points of
`h`

function. - 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`

.

- Calculate the derivatives of the first and second order for the
`h`

function. - Find critical points of
`h`

function. - Check if these critical points are points of the maximum of the function
`h`

.

Everything was clear?

# 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`

.

- Calculate the derivatives of the first and second order for the
`h`

function. - Find critical points of
`h`

function. - Check if these critical points are points of the maximum of the function
`h`

.

Task

We have the following equation:`h = v * t - 0.5 * g * t**2`

that describes the motion of an object.

`t`

when the object reaches its maximum height and then find the maximum height `h_max`

.

- Calculate the derivatives of the first and second order for the
`h`

function. - Find critical points of
`h`

function. - Check if these critical points are points of the maximum of the function
`h`

.

Everything was clear?

# Challenge: Solving the Optimisation Problem

Task

We have the following equation:`h = v * t - 0.5 * g * t**2`

that describes the motion of an object.

`t`

when the object reaches its maximum height and then find the maximum height `h_max`

.

- Calculate the derivatives of the first and second order for the
`h`

function. - Find critical points of
`h`

function. - Check if these critical points are points of the maximum of the function
`h`

.

Task

We have the following equation:`h = v * t - 0.5 * g * t**2`

that describes the motion of an object.

`t`

when the object reaches its maximum height and then find the maximum height `h_max`

.

- Calculate the derivatives of the first and second order for the
`h`

function. - Find critical points of
`h`

function. - Check if these critical points are points of the maximum of the function
`h`

.

Everything was clear?

Task

We have the following equation:`h = v * t - 0.5 * g * t**2`

that describes the motion of an object.

`t`

when the object reaches its maximum height and then find the maximum height `h_max`

.

- Calculate the derivatives of the first and second order for the
`h`

function. - Find critical points of
`h`

function. - Check if these critical points are points of the maximum of the function
`h`

.