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This answer has 3 steps:1) find the derivative, f’(x), of the function2) factorise the derivative 3) set equal to zero and solve for x1) f’(x) = 3x^2 + 6x - 242)f’(x) = 3(x^2 + 2x - 8)3) x^2 + 2x - 8 = 0 ...

For f(x) not to have any real roots, its discriminant, b²-4ac < 0. Plugging in the coefficients from f(x), this means (-(2c+8))²-4x4x4 < 0.This means (-(2c+8))² <...

We know that two vectors are perpendicular when their dot product is equal to 0. As you can see from the SQA Higher Maths formula sheet, the equation for the dot product is; A.B=a1b1+a2b2+a3b3.To...

From the equation x²+y²-8x+10y+41=0, we can find the centre of the circle by the middle two terms -8x+10y and multiplying them by -1/2. So the coordinates of the circle centre are (4...

We know 2 equations for a straight line; Y=MX+C and Y-B=M(X-A). Since we do not have the y intercept (C) or any means of finding it but we do have 2 points on the straight line, it would make sen...