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Differentiate C:dy/dx=4x+5When x=1dy/dx=4(1)+5dy/dx=9This is gradient of tangent.Gradient of normal=-1/9When x=1, y=4y-4=-1/9(x-1)y=(-1/9)x+(37/9)(-1/9)x+(37/9)=2x^2+5x-30=2x^2+(46/9)x-(64/9)x=1 or x=-32/...

In order to differentiate a number, 2 steps are needed to be made. The first is to reduce the power of the number by 1 and then multiply that value to the first number. I will run you through the given qu...

Start with the given equation from the question and differentiate it with respect to x to give you:dy/dx = 2x - 1The value of this gives you the slope of the curve and we know that the minimum point has a...

We know that a stationary point is found when the gradient of the curve is equal to zero, this is found by equaling the derivative (dy/dx) equal to zero. Differentiating the expression will find a quadrat...

For the first part of the question we need to try and understand what is actually happening – we have the sum of an integral – where we are summing a sequence of definite integrals. So when n = 0 we have ...