Search over 10,000 free study notes

Two distinct real roots means that we can use b^2-4ac>0 relationship for any ax^2+bx+c equation. Apply the above gives, 4k^2 - 42(k+2)>0 Simplifying gives, k^2 - 2k -4 >0

To find the stationary points of a function we must first differentiate the function. The derivative tells us what the gradient of the function is at a given point along ...

y = (2x -3)^3

y = (2x)^3 + 3.((2x)^2)(-3) + 3.(2x).(-3)^2 + (-3)^2 using Pascal's Triangle.

y = 8x^3 - 36x^2 + 54x - 27 

dy/dx = 24x^2 - 72x + 54

at point (1,-1); dy/dx = 24 -7...

There is an initial subtle difficulty to this question, and it highlights understanding of the relationship between natural logarithms and the exponential function. One of the ways to solve this question,...

Try y=Ae^bx diffrentiate this (dy/dx = Abe^bx) and sub into 2dy/dx -5y = 0 to find complementary function. 2Abe^bx - 5Ae^bx = 0 2b - 5 = 0 b = 2.5 Find the particul...