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To find the minimum or maximum we need to find a point on the function where its slope is zero. So, we differentiate f(x) and set it equal to zero: f'(x)=0, f'(x) = 6x -2 = 0, x=1/3 Substitute into f(x) t...

So here we need to use the chain rule in order to differentiate the equation. To start you take the function inside the bracket x²+4x and differentiate it to Du/Dx= 2x + 4 this is known as u. d...

average speed=total distance/time taken ; distance=speed x timeFor the first part of her motion the distance she travelled, d₁=40 x 1/2 (as 30 minutes represent half an hour), so d₁=...

Draw out what the question says. Geometric problems are easier to solve when they can be visualised. First calculate the area of the quarter circle: A = 1/4 \pi r^2Use Pythagoras to calculate the base len...

2sin^2(x) + 3sin(x) = 2cos(2x) + 32sin^2(x) + 3sin(x) = 2(cos^2(x) - sin^2(x) ) + 32sin^2(x) + 3sin(x) = 2(1- 2sin^2(x) ) + 32sin^2(x) + 3sin(x) = 2 - 4sin^2(x) + 36sin^2(x) + 3sin(x) - 5 = 0 let sin(x) =...