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A curve is defined for x>0 as y = 9 - 6x^2 - 12x^4 . a) Find dy/dx. b) Hence find the coordinates of any stationary points on the curve and classify them.

a) y = 9 -6x^2 - 12x^4

dy/dx = -12x - 48x^3

b) At stationary points dy/dx = 0.

-12x - 48x^3 = 0

48x^3 + 12x = 0

4x^3 + x = 0

x (4x^2 + 1) = 0

Either ...

Answered by Olivia W. • Maths tutor

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What is the coefficient of x^2 in the expansion of (5+2x)^0.5?

We the answer in question in the form A(1+B)^0.5 and we can do that by factorising out the 5. This gives 5^0.5(1+0.4x)^0.5. 2. Identify the formula we are going to use ...

Answered by Akinmi A. • Maths tutor

3816 Views

Differentiate y=x^(-1/2)-x

The formula you are given is an equation which is written in terms of x. So we will be differentiating with respect to x.

When differentiating we take the current power and place that in front of ...

Answered by Zarin T. • Maths tutor

3625 Views

Find the first derivative of the line equation y=x^3 + 4

dy/dx = 3x^2

Answered by Harry F. • Maths tutor

3480 Views

Integrate x((x^2)+2) dx

The first step is to multiply out the brackets so the function is in a form that can be integrated. X x X² = X³ then X x 2 is simply 2X. So we are left with X³ + 2X. Both ...

Answered by Benjamin H. • Maths tutor

3178 Views