Notice: This page requires JavaScript to function properly.
Please enable JavaScript in your browser settings or update your browser.
Learn Challenge: Solving the Optimisation Problem | Mathematical Analysis
Mathematics for Data Analysis and Modeling

Swipe to show menu

book
Challenge: Solving the Optimisation Problem

Task

Swipe to start coding

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.

Solution

Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
Everything was clear?

How can we improve it?

Thanks for your feedback!

SectionΒ 3. ChapterΒ 5
single

single

Ask AI

expand

Ask AI

ChatGPT

Ask anything or try one of the suggested questions to begin our chat

close

Awesome!

Completion rate improved to 4.76

book
Challenge: Solving the Optimisation Problem

Task

Swipe to start coding

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.

Solution

Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
Everything was clear?

How can we improve it?

Thanks for your feedback!

close

Awesome!

Completion rate improved to 4.76

Swipe to show menu

some-alt