Geometry, Calculus, Matrices and Surds GCSE Further Maths Worksheets, Questions and Revision

Find dy/dx for the curve y = 2x^4 - 5x^3 + 6x - 9, and hence find the gradient of the curve at the point where x = -1.

1. Differentiate each term: 2x^4 becomes 4 x 2x^3 = 8x^3.
2. -5x^3 becomes 3 x -5x^2 = -15x^2.
3. 6x becomes 6, and the constant -9 becomes 0.
4. So dy/dx = 8x^3 - 15x^2 + 6.
5. Substitute x = -1: 8(-1)^3 - 15(-1)^2 + 6 = -8 - 15 + 6.
6. Final answer: dy/dx = 8x^3 - 15x^2 + 6, and the gradient at x = -1 is -17.