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Maths
A Level

A curve has equation y = 2x^5 + 5x^4 1 . (a) Find: (i) dy/ dx [2 marks] (ii) d^2y/ dx^2 (b) The point on the curve where x ¼ 1 is P. (i) Determine whether y is increasing or decreasing at P, giving a reason for your answer.

a.) dy/dx+10x^4+20x^3

d^2y/dx^2=40x^3+60x^2

b.)sub in x=-1 to dy/dx=10(-1)^4+20(-1)^3

=-10

therefore, decreasing

AF
Answered by Alexandra F. Maths tutor
9403 Views

Explain the Chain Rule

The chain rule is used to differentiate composite functions, ie "a function of a function". In this case we have an outer function and an inner function. For example

Differentia...

AC
Answered by Alex C. Maths tutor
4045 Views

What is the angle between the position vectors a and b, where a = (6i - j + 3k) and b = (-4i + 2j + 10k)?

cos(AOB) = a.b/(|a| x |b|)

a.b = (6i - j + 3k).(-4i + 2j + 10k)

      = (6 x -4...

DH
Answered by David H. Maths tutor
5933 Views

Simplify (5-root3)/(5+root3)

multiply with conjugate 5-root3 such that the denominator gets rational 

(5-root3)^2/((5+root3)(5-root3)) = (25-10root3+3)/(25-3)=(28-10root3)/22 = 14/11 - 5root3/11

EG
Answered by Evita G. Maths tutor
13586 Views

Factorise x^3-6x^2+9x.

x^3-6x^2+9x=x(x^2-6x+9)

observe binomial formula (x-3)^2=(x^2-6x+9)

Thus x(x-3)^2 and the function has two points meeting the x-axis.

EG
Answered by Evita G. Maths tutor
14559 Views

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