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Gradient is change in y divided change in x.As the change shrinks to effectively nothing (as we want to gradient at a point, not between points), we use dy/dx (the derivative of y with respect to x), to w...

y = x + 3x² + 2y = 9We want to make the squared equation have either only x's or only y's, so we substitute y = x + 3 into the equation:x² + 2(x + 3) = 9We need to take out the brack...

STEP 1: Prove that the theorem holds for n = 1. Substitute n = 1 into the equation and show that the LHS = RHS.
STEP 2: Assume that the relation is true when n = k.
STEP 3: Prove that the relat...

For any mechanics question such as this one the best way to start off is by drawing a diagram of the system and including all the forces acting on the pa...

At stationary point the derivative of y with respect to x equals zero. Find dy/dx. dy/dx = 2x - 6x^2.Set dy/dx = 0 ,giving 2x - 6x² = 0. We can rearrange this to x(1-3x) = 0 and solve...