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Solve these simultaneous equations: 2x + y = 7, and 3x - y = 8. Do so by 1) Eliminating an Unknown and 2) Substitution.

The number 'in front of' an unknown is called the Coefficient. When eliminating an unknown, look to see whether the coefficients of x are the same in both equations, or if the coefficients of y are the same....
EH
Answered by Ellie H. • Maths tutor
3919 Views

(1.) f(x)=x^3+3x^2-2x+15. (a.) find the differential of f(x) (b.) hence find the gradient of f(x) when x=6 (c.) is f(x) increasing or decreasing at this point?

(1.) (a.) f’(x)=3x^2+6x-2 (b.) x=6 gradient=142 (c.) since f’(x)>0 at x=6, the function is increasing.
JE
Answered by Joel E. • Maths tutor
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The equation x^3 - 3*x + 1 = 0 has three real roots; Show that one of the roots lies between −2 and −1

In order to prove that one real root of an equation is situated in a certain interval, we calculate the value of the function at the ends of the given interval. In the given case, f(-2) = (-2)^3 - 3*(-2) + 1...
PT
Answered by Paul T. • Maths tutor
12737 Views

Complete the square and find the roots (where y=0) of: "x^2+4x-5"

completing the square: (x+2)^2-9 finding the roots: (x+2)^2=9 x+2=+/-3 at y= 0, x= -5 or 1
LQ
Answered by Liam Q. • Maths tutor
4651 Views

y=4x^3+6x+3 so find dy/dx and d^2y/dx^2

dy/dx=12x^2+6 d^2y/dx^2=24x
SP
Answered by Swapnil P. • Maths tutor
5541 Views