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Show that the funtion (x-3)(x^2+3x+1) has two stationary points and give the co-ordinates of these points

Stationary points are points where the gradient of a function is equal to 0. In this question the product rule can be used to find the gradient of the given function. The product rule is given by u'v+uv'...

Answered by Joe R. • Maths tutor

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Find the nature of the turning points of the graph given by the equation x^4 +(8/3)*x^3 -2x^2 -8x +177 (6 marks)

(1 mark) Differentiate equation in the question: 4x³+8x²-4x-8(1 mark) Equate this to zero: (x-1)(x+1)(x+2)=0(1 mark) Find turning points (roots of above equation): x=1,-1,-2(1 mark) ...

Answered by Elizabeth B. • Maths tutor

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show that y = (kx^2-1)/(kx^2+1) has exactly one stationary point when k is non-zero.

Stationary points are found by considering the points at which the gradient of the function equal zero. For the above, you need to employ the quotient rule, since both numerator and denominator are f(x), ...

Answered by Rob M. • Maths tutor

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A ball is projected vertically upwards from the ground with speed 21 ms^–1. The ball moves freely under gravity once projected. What is the greatest height reached by the ball?

Set out information given in question, and taking the upward direction to be positive: s (displacement) = ?, u (initial speed) = 21ms^-1, v (final speed at maximum height) = 0ms^-1, a ...

Answered by Shruti S. • Maths tutor

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Solve 7x + 6 > 1 + 2x

7x + 6 > 1 + 2xFirst, we collect the like terms so we move all the x's to one side and all the integers to the other:5x > -5Then we divide by 5 on each side to find what just x will be.Therefore, x ...

Answered by Juliet Z. • Maths tutor

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