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solve 15x = 6x^3 + 8x^2

6x³ + 8x² -15x = 0x(6x² + 8x - 15) = 0x=06x² + 8x - 15 = 0Quadratic formula ( can demonstrate in interview)x = 0 or x = 1.049 or x = -2.38

Answered by Lewis L. • Maths tutor

2637 Views

The function f has domain (-∞, 0) and is defines as f(x) = (x^2 + 2)/(x^2 + 5) (here ^ is used to represent a power). Show that f'(x) < 0. What is the range of f?

First notice that f(x) = u/v. So f'(x) =[ v(u') - u(v')]/v² (the Quotient rule). After working it out, we find f'(x) = 6x/(x²+ 5)²(the steps can be shown on the whiteboa...

Answered by Chris C. • Maths tutor

2768 Views

Given that y = (1 + 3x^2)^(1/3) , use the chain rule to find dy/dx in terms of x.

Take u = 1+3x² , this gives that y = u^1/3. By the chain rule we have that dy/dx = dy/du * du/dx. By differentiating y = u^1/3 with respect to u giv...

Answered by Jasmine S. • Maths tutor

4668 Views

find the second degree equation that passes through the points: (0,1) (2,2) (1,0)

first of all we have to recognise the general form of the equation, similar to the equation of a line but we just have to add one more term due to the fact that it is a second degree equation: y=ax^2<...

Answered by Luca G. • Maths tutor

2891 Views

Integrate ln(x).

For this you’ll want to use the integration by parts method. In this the form u use is:integral of udv = uv - integral of vduTherefore we can rewrite the integral as ln(x)*1 labelling 1 as dv and ln(x) as...

Answered by Euan S. • Maths tutor

1561 Views