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Find the value of the discriminant of x2 + 6x + 11

For a quadratic equation in the form ax^2+bx+c=0 the determinant is given by b^2-4ac and is used to help identify the types of roots of the equation. In this case, the determinant is (6)^2-4(1)(11) which is ...
EC
Answered by Emily C. • Maths tutor
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Find the derivative of the function y=3x^2e^(2x)sin(x).

y is the product of three different function, so we would use the product rule in order to calculate the derivative of the curve. In order to apply the product rule we need to find the derivatives of each of...
SR
Answered by Shreya R. • Maths tutor
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f(x)=(2x+1)/(x-1) with domain x>3. (a)Find the inverse of f(x). (b)Find the range of f(x). (c) g(x)=x+5 for all x. Find the value of x such that fg(x)=3.

(a) Let y=f(x). Then y = (2x+1)/(x-1). Rearrange the equation to get x in terms of y to obtain the inverse function. This gives x=(1+y)/(y-2). So the inverse of f is f -1 (x)=(1+x)/(x-2) (b) Drawing a graph ...
LA
Answered by Lutfha A. • Maths tutor
5876 Views

Find dy/dx for y = x^3*e^x*cos(x)

In this problem, we see that y is a product of 3 functions of x. That means that in order to find dy/dx we need to use the product rule. The product rule tells us that in this case we should differentiate on...
LN
Answered by Lyudmil N. • Maths tutor
10584 Views

Solve x² ≥ | 5x - 6 | (Question from AQA Core 3 June 2016)

To solve this question we can break it down in to a multiple small stages. The first thing to tackle is the use of modulus around 5x - 6. This effectively means we have two equations to solve: EQ1: x² ≥ 5x -...
JH
Answered by James H. • Maths tutor
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