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Find the x-values of the turning points on the graph, y=(3-x)(x^2-2)

The minimum point occurs where dy/dx=0

We have 2 options: 1.) Expanding the brackets 2.) The product rule of differentiation

The shortest is the product rule: dy/dx= (d/dx)(3-x).(x²

Answered by Zita E. • Maths tutor

2757 Views

The height (h) of water flowing out of a tank decreases at a rate proportional to the square root of the height of water still in the tank. If h=9 at t=0 and h=4 at t=5, what is the water’s height at t=15? What is the physical interpretation of this?

Note: time, t, is measured in minutes, and height, h, is measured in metres.

Let k>0, a constant.

The differential equation to be solved is given by: dh/dt = - k(h)^0.5.

Us...

Answered by Sandie N. • Maths tutor

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curve C with parametric equations x = 4 tan(t), y=53^(1/2)sin(2t). Point P lies on C with coordinates (4*3^(1/2), 15/2). Find the exact value of dy/dx at the point P.

dy/dx = dy/dt *dt/dx (chain rule).

x=4tan(t) hence dx/dt = 4 sec²(t)

y = 53^1/2sin(2t) hence y'= 103^1/2 cos(2t)

therefore dy/dx = 103^...

Answered by Harry P. • Maths tutor

7129 Views

Find the first derivative of r=sin(theta+sqrt[theta+1]) with respect to theta.
To find the first derivative we must apply the chain rule. Our aim is to find dr/d(theta). We start by bringing the differential of what's inside the sine brackets outside and multiplying it by the differ...
Answered by Tutor61926 D. • Maths tutor
4232 Views

Perhaps an introduction to integration with a simple integral, e.g. the integral of x^2
I would first write out the integral with correct notation, explaining to my tutee exactly what I am drawing and why. I will then explain the 'n+1' rule for integrating simple powers. I will go through th...
Answered by Reece C. • Maths tutor
2974 Views

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Find the x-values of the turning points on the graph, y=(3-x)(x^2-2)

The height (h) of water flowing out of a tank decreases at a rate proportional to the square root of the height of water still in the tank. If h=9 at t=0 and h=4 at t=5, what is the water’s height at t=15? What is the physical interpretation of this?

curve C with parametric equations x = 4 tan(t), y=53^(1/2)sin(2t). Point P lies on C with coordinates (4*3^(1/2), 15/2). Find the exact value of dy/dx at the point P.

Find the first derivative of r=sin(theta+sqrt[theta+1]) with respect to theta.

Perhaps an introduction to integration with a simple integral, e.g. the integral of x^2

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© MyTutorWeb Ltd 2013–2025

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Search over 10,000 free study notes

Top answers

Find the x-values of the turning points on the graph, y=(3-x)(x^2-2)

The height (h) of water flowing out of a tank decreases at a rate proportional to the square root of the height of water still in the tank. If h=9 at t=0 and h=4 at t=5, what is the water’s height at t=15? What is the physical interpretation of this?

curve C with parametric equations x = 4 tan(t), y=5*3^(1/2)*sin(2t). Point P lies on C with coordinates (4*3^(1/2), 15/2). Find the exact value of dy/dx at the point P.

Find the first derivative of r=sin(theta+sqrt[theta+1]) with respect to theta.

Perhaps an introduction to integration with a simple integral, e.g. the integral of x^2

We're here to help

Company Information

Popular Requests

© MyTutorWeb Ltd 2013–2025

CLICK CEOP

curve C with parametric equations x = 4 tan(t), y=53^(1/2)sin(2t). Point P lies on C with coordinates (4*3^(1/2), 15/2). Find the exact value of dy/dx at the point P.