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The normal to the curve C when x=1 intersects the curve at point P. If C is given by f(x)=2x^2+5x-3, find the coordinates of P

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/...

Answered by Hannah C. • Maths tutor

3234 Views

Differentiate 3x^2 + 4x - 7

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...

Answered by James R. • Maths tutor

4723 Views

Find the coordinates of the minimum point on the curve: y = x^2 - x - 2

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...

Answered by Alex R. • Maths tutor

4514 Views

A curve has an equation of y = 20x - x^2 - 2x^3, with one stationary point at P=-2. Find the other stationary point, find the d^2y/dx^2 to determine if point P is a maximum or minium.

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...

Answered by Georgia S. • Maths tutor

2789 Views

Consider the infinite series S=Σ(from n=0 to infinite) u(down n) where u(down n)=lim (from n π to (n+1) π) ((sin t)/t) dt. Explain why the series is alternating.

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 ...

Answered by Stuart D. • Maths tutor

5455 Views