Unit 7 (graphing trig and calculus)

rate of change, derivatives, tangent and normal lines

major focus

rate of change- to find the change rate of y with respect to x.

derivatives and tangent lines- used to find the gradient of the curve.

normal lines- are perpendicular to the tangent line at point of tangency.

curve- the curve is used to solve for maximum and minimum problems.

formulas

derivative- dy/dx or ax^(n)= nax^(n-1)

normal line- when y=x then normal is y=-1/x

x<1/2 the gradient is negative (decreasing)

x>1/2 the gradient is positive (positive)

x=1/2 the gradient is zero not increasing or decreasing

problems and graphs

definitions

definitions

derivative- the formula used to find the curve of a line.

tangent-a straight line that touches the curve at one point representing the rate of change when the derivative equals the original equation.

normal- a line that is perpendicular to the tangent line at the point of tangency.

maximum-the highest point on a graph.

minimum-the lowest point on a graph.

hints

the formula of the tangent is y=mx+c

c can be found using algebra

the normal line is perpendicular to the tangent line.

the gradient of the normal line is the opposite reciporicle of the tangent line.