Top answers

Find the roots of the following quadratic equation: x^2 +2x -15 =0

The question asks for the roots, this simply means the numbers that could replace x in the equation and the result = 0. There are two ways too do this, firstly either using the Quadratic formula, or my facto...
Answered by • Maths tutor
4996 Views

Consider the function f (x) = (2/3) x^3 + bx^2 + 2x + 3, where b is some undetermined coefficient: (a) find f'(x) and f''(x) and (b) if you know that f(x) has a stationary point at x = 2, use this information to find b.

(a) We have f(x)=(2/3)x 3 + bx 2 + 2x +3. First we have to solve for f'(x)=(dy/dx)f(x) which gives:f'(x) = [(3 2)/3]x 2 + 2bx + 2 <=> f'(x)=2x 2 + 2bx + 2 From there we do a second differentiation to s...
Answered by • Maths tutor
3870 Views

Show that x^2+6x+11 can be written in as (x+p)^2+q, where p and q are integers to be found.

To start, we need to complete the square of the equation. To do this, we divide the coefficient of x by 2. Here, 6/2=3. We then find (x+3)^2, which gives us the first part of the equation we want to express,...
HE
Answered by Hannelore E. • Maths tutor
10527 Views

How do I find the co-ordinates of a stationary point of a given line and determine whether it is a minimum or a maximum point?

When you find the first derivative of the equation and equate it to 0 then solve for x, you will find the x-coordinates of the stationary point(s) of the graph. For example, let's say f(x)=-x 3 +x 2 +8x+10 t...
Answered by • Maths tutor
4327 Views

How do you find the first order derivative of sin(x) and cos(x) functions?

The general rules are:d(sin x)/ dx = cos xd(cos x)/ dx = -sinxHowever, if you have a constant k in the function such as y = sin(kx), the derivative will be dy/dx = kcos(kx). (For y = cos(kx), the derivative ...
NS
Answered by Niusha S. • Maths tutor
5352 Views