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A curve C has equation y = x^2 − 2x − 24 x^(1/2), x > 0 (a) Find (i) dy/d x (ii) d^2y/dx^2 (b) Verify that C has a stationary point when x = 4 (c) Determine the nature of this stationary point, giving a reason for your answer.

(a) i) dy/dx= 2x-2-12x^-1/2ii) d²y/dx²= 2+6x^-3/2(b) Substitute x=4 into dy/dx= 2x-2-12x^-1/2 Show that dy/dx= 0 and state 'hence there is a stationar...

Answered by • Maths tutor

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Work out the cube root of (64x1000).

We are asked to calculate (64x1000)^1/3. We can use the laws of indices to write that expression as 64^1/3x1000^1/3, which is easier to evaluate. To work out 64^1/3...

Answered by Martin P. • Maths tutor

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f ( x ) = 2 x ^3 − 5 x ^2 + ax + a. Given that (x + 2) is a factor of f ( x ), find the value of the constant a. (3 marker)

If x+2 is definitely a factor, that means when we sub x=-2 in, we should get 0 at the end. So 2(-2)^3 - 5(-2)^2 + a(-2) + a = 0So -16 -20= aso a = -36

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Use the quadratic formula to find the solutions to x^2+2x-35=0

x=5 and x=7

Answered by Georgia N. • Maths tutor

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The perimeter of a right-angled triangle is 72 cm. The lengths of its sides are in the ratio 3 : 4 : 5 Work out the area of the triangle.

The equation for the area of a triangle is 1/2 x base x height
So, first we need to know the length of the base and the height of the triangle.
We know that the perimeter of the triangle is 72...

Answered by Alison B. • Maths tutor

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