Answers>Further Mathematics>A Level>Article

A curve C has equation y = x^2 − 2x − 24 x^(1/2), x > 0. Find dy/dx and d^2y/dx^2. Verify that C has a stationary point when x = 4

Using the differentiation rule that d (Ax^b)/dx = Abx^(b-1) we find dy/dx = 2x -2 -12x^(-1/2).Similarly, taking care to see that the -2 term becomes zero since it is not dependent on x, we haved^2y/dx^2 = 2 + 6x^(-3/2).By substituting the value x = 4 into our expression of dy/dx we have2x4 -2 -12x(4^(-1/2)) = 0. Hence we have a stationary point at the value x = 4.

Answered by Alexa W. • Further Mathematics tutor

3187 Views

A curve C has equation y = x^2 − 2x − 24 x^(1/2), x > 0. Find dy/dx and d^2y/dx^2. Verify that C has a stationary point when x = 4

Related Further Mathematics A Level answers

Does the following matrix A = (2 2 // 3 9) (upper row then lower row) have an inverse? If the matrix A^2 is applied as a transformation to a triangle T, by what factor will the area of the triangle change under the transformation?

Prove by induction that 1^2 + 2^2 + 3^2 + . . . + n^2 = (1/6)n(n+1)(2n+1)

The point D has polar coordinates ( 6, 3π/4). Find the Cartesian coordinates of D.

Using z=cos(θ)+isin(θ), find expressions for z^n-1/z^n and z^n+1/z^n