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We will figure out the general question first: if we have n consecutive events with two possible outcomes which we will tell "successes" and "failures" with probabilities p and 1-p, re...

Differentiate to get dy/dx=20-2x-6x^2Then stationary points occur when dy/dx = 0 so 0 = 20-2x-6x^2 Factorise to get x= -2, x=5/3Differentiate dy/dx to get second derivative = -2-12x at x=5/3 is -22 so max...

Take the graph y = x² - 2x + 5 for example:
In order to find the intersection with the y axis, set the x values in the equation equal to 0 as this is where the graph would cross the y axi...

dy/dx = u.dv/dx + v.du/dxu = x³, v = ln xdu/dx = 3x², dv/dx = 1/xdy/dx = 3x² lnx + x²