Chapter 14

Question 1

Define normal to a curve.

Answer 1

A straight line which crosses the curve at a given point and is perpendicular to the tangent.

Question 2

How do you work out the equation of a tangent or normal to a curve y = f(x) with x = a?

Answer 2

.Tangent gradient = f’(a).
.Normal gradient = -1/f’(a).
.Coordinates are x1 = a, y1 = f(a).
.y - y1 = m(x - x1) for equation.

Question 3

How do you find the local minimum/maximum points of a curve.

Answer 3

Sole dy/dx = 0.

Question 4

With a stationary point (x0, y0) and function y = f(x), how to you determine if it’s a minimum or maximum?

Answer 4

.If d2y/dx2 < 0 - maximum.
.If d2y/dx2 > 0 - minimum.
.If d2y/dx2 = 0 - no conclusions drawn.

Question 5

What are the two common types of constraint?

Answer 5

.Shape with fixed perimeter/area/volume.
.Point lying on a given curve.