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What is the gradient of the curve y = 2x^3 at the point (2,2)?

Firstky differentiate to gain an equation for the gradient.Differentiating gives:dy/dx = 6x 2 Insert x = 2 into the above equation to find the gradient at that particular point of the curve.When x = 2, dy/dx...
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Answered by Emily R. • Maths tutor
8749 Views

Show that the curve y =f(x) has exactly two turning points, where f(x)= x^3 - 3x^2 - 24x - 28

This question is about turning points of a curve, these occur when the gradient of a line is zero. In its current form, the equation of the curve tells us nothing about the gradient of the curve; it must be ...
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Answered by Joshua A. • Maths tutor
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Issy goes to buy some fruit. She has been told by one friend that 2 apples and 3 bananas costs £3.80. She has been told by another friend that 5 apples and a banana costs £3.65. what are the individual costs of an apple and a banana?

To solve this we form two simultaneous equations. To make things easier lets denote apples as A and bananas as B. So this means we can write the above information in two equations like so: EQ1) 2A + 3B = 380...
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Answered by Kieren H. • Maths tutor
5244 Views

Two simultaneous equations are given as 2x + y = 5 and 3x + y = 7. Find the value of x and y.

The unknowns of x and y are the same in each equation, allowing us to combine the two in order to find out their values.The substitution method can be used in most cases if the coefficient is the same with x...
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Answered by Megan H. • Maths tutor
4610 Views

How would you differentiate and integrate 2x^3?

Integration is the opposite of differentiation.First of all take your 2x 3 So in differentiation you would times the power by the coefficient and then minus one from the power.This would give,6x 2 in other w...
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Answered by Scarlett K. • Maths tutor
8349 Views