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Find the gradient of the tangent to the curve with the equation y = (3x^4 - 18)/x at the point where x = 3

y = (3x 4 - 18)/x The gradient of a tangent to a curve is equal to dy/dx However, we must simplify this equation before we can differentiate it; y = 3x 3 - 18/x = 3x 3 - 18x -1 dy/dx = 3(3x 2 ) - (-1)(18x -2...
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Answered by Rachel O. • Maths tutor
5069 Views

Find the difference between the areas of these 2 shapes to 2 decimal places. Rectangle (width 4cm length 2.5cm) Circle (diameter 2.4) use pi = 3.14

Rectangle: Area = width x length hence area = 4cm x 2.5cm area = 10cm 2 Circle: Area = pi x radius 2 Radius = 1/2 x diameter Radius = 1.2cm Area = 1.2 2 x 3.14 Area = 1.44 x 3.14 Area = 4.5216 Difference bet...
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Answered by Lyam H. • Maths tutor
9060 Views

Find the turning points of the curve y = x^3 +5x^2 -6x +4

y = x 3 +5 x 2 -6 x +4 dy/dx = 3 x 2 +10 x -6 at turning points dy/dx = 0 therefore 3 x 2 +10 x -6 = 0 This quadratic is factorisable. When factorised you get: (3 x -2)( x +4) = 0 therefore x = 2/3 and -4 at...
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Answered by Arshan B. • Maths tutor
20312 Views

Differentiate y=x^3

dy/dx = 3x^2
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Answered by Rhiannon H. • Maths tutor
5536 Views

If the area of a rectangle with sides 3cm and (4+x)cm is equal to that of a triangle with base of 2xcm and a height of 4cm, find x

First, if the question does not already have one, draw a diagram. Area of a rectangle is base * height and area of a triangle is 1/2 * base * height. As the two areas are the same, you know you can set the t...
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Answered by Alice K. • Maths tutor
4962 Views