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The line y = (a^2)x and the curve y = x(b − x)^2, where 0<a<b , intersect at the origin O and at points P and Q. Find the coordinates of P and Q, where P<Q, and sketch the line and the curve on the same axes. Find the tangent at the point P.

Firstly, for the points of intersection we need to equate the two expressions for y. Since we know that they intersect at the origin, we can immediately cancel the x values and then solve the quadratic for t...
JB
Answered by Josh B. • Maths tutor
7209 Views

Use completing the square to find the minimum of y = x^2 - 4x + 8

Remember completing the square gives a result of the form (x+q) 2 + p where q and p are numbers Also q is always half of the x term, which in this case is -4, as such q = -2 Substituting this in, we get (x-2...
SD
Answered by Sol D. • Maths tutor
3683 Views

2 5/3 + 2 8/9

2 5/3 = 11/32 8/9 = 24/9 = 8/311/3 + 8/3 = 19/3 = 6 1/3
HR
Answered by Huw R. • Maths tutor
3086 Views

Solve the equation 3x^2+2x-3=3.

rearrange the formula so that it is equal to zero by subtracting 3 from both sides of the equation.3x 2 +2x-6=02) To check if this formula can be factorised you can check if the value of b 2 -4ac for this fo...
JB
Answered by Jolie B. • Maths tutor
4674 Views

Find the equation of the tangent to the curve y = 4x^2 (x+3)^5 at the point (-1, 128).

y = 4x 2 (x+3) 5 . Use the product rule to find the first derivative of the curve, 8x(x+3) 5 + 20x 2 (x+3) 4 , and substitute x = -1 to find the gradient at the point (-1, 128). This should be 64. Now substi...
JG
Answered by Jack G. • Maths tutor
3881 Views