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How do you find the equation of a tangent to a curve at a certain point, from the equation of the curve?

First thing you would do is write down the coordinates where the tangent meets the curve. After that you would differenciate the equation (f(x)) of the curve (do dy/dx) in order to get f'(x).Then you would s...
AO
Answered by Antoine O. • Maths tutor
4090 Views

John wants to separate a rectangular part of his garden for his puppy. He has material for a 100-meter long fence and he plans to use one side of his house as a barrier. How should John select the sizes of his fence in order to gain the biggest territory?

We can denote the sides of the rectangle with a and b. As one side of the separated area is going to be the wall of the house, we do not have to use a fence there. Therefore, we will have two sides, one deno...
SG
Answered by Soma G. • Maths tutor
3332 Views

Why is the derivative of sin(x), cos(x)?

Find out what they know what the questions means, ie if they know what sinx and cosx are and then how much they understand about what derivatives are.I would explain from the point they're at, define everyth...
RA
Answered by Ryan A. • Maths tutor
4008 Views

f(x) = x^3 + 3x^2 + 5. Find (a) f ′′(x), (b) ∫f(x)dx.

(a) To find the second derivative of f(x) we must differentiate f twice.the first derivative of f is f'(x)= 3x^2 + 6xthe second derivative therefore is f''(x)= 6x +6 (b) The integral of f(x) with respect to ...
SC
Answered by Samraj C. • Maths tutor
8398 Views

How would you solve 4x > 7 - 10x ?

When solving an inequality, you want to get all of the x terms on one side, just like when you're solving an equation. Therefore, adding 10x to each side would give us:4x (+10x) > 7 - 10x (+10x) which giv...
SG
Answered by Sarah G. • Maths tutor
3693 Views