Foundations of Computing II: Gradients & Differentiation

These flashcards cover key concepts from the lecture on gradients and differentiation, including the calculation of gradients, the equations of tangents and normals, and differentiation rules.

What is the formula to calculate the gradient of a straight line between points P and Q?

Gradient m = (y2 - y1) / (x2 - x1)

How do you find the equation of a straight line given the gradient and a point?

Use the formula: y - y1 = m(x - x1)

What does the gradient of a straight line represent in a distance-time graph?

The gradient represents the speed.

What is the first step to find the gradient of a curve at point P?

Draw a tangent to the curve at point P.

What is the Power Rule in differentiation?

For y = x^n, d/dx(y) = n*x^(n-1).

What is the significance of the equation of the tangent to the curve at point P?

It gives the slope of the curve at that point and can be used to create linear approximations.

What is the formula to find the equation of the normal line to a curve?

The normal line has a gradient that is the negative reciprocal of the tangent's gradient.

How is the gradient of the tangent to the curve y=x^2 at point P= (2,4) calculated?

It is calculated as m = 2*2 = 4.

What do the terms 'dydx' and 'δy/δx' represent?

They represent the derivative of y with respect to x.

What is the equation of the normal to the curve y = x^2 at the point P = (2,4)?

The equation of the normal is y = -0.25x + 4.5.