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steps as follows:x times x = x²2 times 5 = 102 times x = 2xx times 5 = 5xthen add these together:y = x² + 7x +10x = -2, -5; y = 0, 10

Use implicit differentiation on original equation-
12x + 3x(dy/dx) + 3y - 2y(dy/dx) = 0
dy/dx= -12x -3y/(3x-2y) at A, x= -5 and y= 10 therefore, dy/dx=-6/7

To find the normal of t...

This requires the chain rule and the product rule to be used to differentiate the function. The substitution u = x² can be used to make this easier. Using this, du/dx = 2x and y = (u-5)e^u<...

This is what we call a quadratic equation. To solve, first we need to factorise this equation into two brackets. (x + _ )(x + _) =0To fill the brackets, we need to find 2 numbers that add to 11 and multip...

To find a local minimum (i.e. a point where the function changes from a negative slope into a positive slope), we first need to find all points where the slope of the function is zero. The first derivativ...