A ball is thrown in the air. The height of the ball at time t is given by: h=5+4t-2t^2. What is its maximum height? At what time does the ball reach this height?

First, we find the derivative of h: dh/dt= 4-4t. To find the point(s) of interest, we solve dh/dt=0. This gives the answer t=1. In order to determine whether t=1 is a minimum point or maximum point we find the second derivative of h: d2h/dt2=-4. As the second derivative of h is less than 0, this shows that there is a maximum point at t=1. Therefore, the ball reaches its maximum height when t=1. To determine the maximum height, we substitute t=1 into the equation for h. Here, we find the maximum height achieved by the ball is h=7.

Answered by Debbie S. Maths tutor

4090 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate x^3⋅cos(5⋅x) with respect to x.


Make x the subject of the equation: 5x+1 = 2-4x


The quadratic equation (k+1)x^2 + (5k - 3)x + 3k = 0 has equal roots. Find the possible values of k


Differentiate 2x/cos(x)


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences