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• Level: GCSE
• Subject: Maths
• Word count: 7101

# I am going to investigate the gradients of different curves and try to work out a pattern that I could use to find the gradient of any curve.

Extracts from this document...

Introduction

Middle

Conclusion

Evidence to support this comes from looking at the result for y = 7x2 +4x + 5. Part Three: x3 and x3 + x graphs Equation Gradient Value of a Value of b 3ax2 + b y = x3 3x2 1 0 3x2 y = 2x3 6x2 2 0 6x2 Test: y = 4x3 + 2x - 5 12x2 + 2 4 2 12x2 + 2 If the number in front of x3 is called 'a' and the number in front of x is called 'b', then I have found that the gradient of this type of curve is always given by 3ax2 + b. Evidence to support this comes from looking at the result for y = 4x3 + 2x - 5. I can summarise these results in a single table. Part of equation Part of gradient formula ax3 3ax2 bx2 2bx cx c d Not present Prediction x4 4x3 This means that I can find the gradient of any curve involving x3, x2, x and a number at any value of x. Sample equation Formula for gradient Gradient at x = 1 y = x3 - 2x2 + 4x - 1 3x2 - 4x + 4 3 - 4 + 4 = 3 y = 2x3 - x2 + 5x -5 6x2 - 2x + 5 6 - 2 + 5 = 9 y = 3x3 + 2x2 - 2x + 3 9x2 + 4x - 2 9 + 4 - 2 = 11 y = 4x3 - 2x2 + 6x - 1 12x2 - 4x + 6 12 - 4 + 6 = 14 y = 5x3 + x2 + 2x + 1 15x2 + 2x + 2 15 + 2 + 2 = 19 SUMMARY The formula for gradient involves taking the power of x and multiplying it by x to one less power. y = Dxb gradient = bDxb - 1 Aidan Casey 11CS 1 ...read more.

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