Top answers

4^x - 2^x+1 - 15 = 0

x = log5/log2
NE
Answered by Narhen E. • Maths tutor
3296 Views

For the curve y = 2x^2+4x+5, find the co-ordinates of the stationary point and determine whether it is a minimum or maximum point.

Stationary points occurs when the gradient of the graph is equal to 0, i.e. dy/dx = 0. Differentiate y with respect to x to get dy/dx = 4x + 4.So making 4x + 4 = 0 gives x = -1. Substituting this into the or...
OB
Answered by Owen B. • Maths tutor
5806 Views

Find the x co-ordinate of stationary point of the graph y=5x^3 +3x

When you differentiate the function that gives the gradient. Therefore differentiate to get dy/dx= 15x^2 + 3. Make this equal to 0 to get 15x^2 + 3=0 and rearrange to get the value of x as required so 15x^2=...
VJ
Answered by Vinay J. • Maths tutor
3867 Views

Integrate ln(x)

Our A-level knowledge does not give us any identities to be able to integrate this from memory. But what we do have from memory is that the derivative of ln(x) is 1/x. Why would this help us? Let's take a lo...
JE
Answered by James E. • Maths tutor
3619 Views

Consider the unit hyperbola, whose equation is given by x^2 - y^2 = 1. We denote the origin, (0, 0) by O. Choose any point P on the curve, and label its reflection in the x axis P'. Show that the line OP and the tangent line to P' meet at a right angle.

We differentiate our equation with respect to x to find that 2x - 2y(dy/dx) = 0, and rearrange to find that dy/dx = x/y. We set P = (x, y). The slope of OP is given by y/x, and the slope of the tangent at P'...
DC
Answered by Dylan C. • Maths tutor
3847 Views