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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
7216 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
3885 Views

How do I use the product rule for differentiation?

You should use the product rule when you have a function f(x), which you can't differentiate straight away. But which can be written in the form f(x)=g(x)h(x), where g(x) and h(x) are functions that you do k...
HV
Answered by Harry V. • Maths tutor
3344 Views

y = 4(x^3) + 7x ... Find dy/dx

This is a simple differentiation question. To start, you need to know the general method of differentiation. This is: if y = Axb then dy/dx = (A*b)x b-1 There are two terms to differentiate in this problem, ...
EE
Answered by Emilio E. • Maths tutor
3927 Views

Given that A(sin θ + cos θ) + B(cos θ − sin θ) ≡ 4 sin θ, find the values of the constants A and B.

Since this must be true for all values of θ, and cos and sin are distinct functions, no non-zero multiple of cosθ could ever be equal to 4 sinθ for all values of θ. Therefore, the overall multiple of cosθ on...
DB
Answered by David B. • Maths tutor
8564 Views