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The line y=5-x intersects the curve y=x^2-3x+2 at the points P and Q. Find the (x,y) coordinates of P and Q.

Step 1: To find the points of intersection, we must find where the y and x values are equal. Therefore 5-x=x²-3x+2 where the y-values are equal.

Step 2: Rearrange the above into the quad...

Answered by Georgina B. • Maths tutor

21079 Views

The polynomial p(x) is given by p(x)=x^3 - 5x^2 - 8x + 48. Given (x+3) is a factor of p(x), express p(x) as a product of 3 linear factors.

This answer is easiest explained using the whiteboard in the interview. The question is basically asking for algebraic long division, we know (x+3) is a factor and are tasked with finding the other 2. We ...

Answered by Richard M. • Maths tutor

3964 Views

Find the equation of the tangent to the curve y = (5x+4)/(3x -8) at the point (2, -7)

(Much easier to explain in conversation and with drawings): But,

An application of the quotient rule, stating that for f(x)=a(x)/b(x), f'(x) = a'(x)b(x) - a(x)b'(x) all over [b(x))]^2 Here, a(x) =...

Answered by Ben R. • Maths tutor

5493 Views

If y=cos(3x)cosec(4x), find dy/dx.

Use the product rule: Let u = cos3x , v = cosec4x Then du/dx = -3sin3x , dv/dx = -4cosec4xcot4x (standard result, given in the formula booklet) Hence dy/dx = -4cosec4xcot4xcos3x - 3sin3xcosec4x . (...

Answered by Pria D. • Maths tutor

4353 Views

Find the coordinates of the turning point of y=e^(2x)*cos(x)?

Think about which process we need to determine the turning point? - Differentiation
Think about the form of the given function. - Product of two functions, so use Product Rule...

Answered by Abbas H. • Maths tutor

6814 Views