ap calc unit 2- derivatives

the slope of a function =

• Δy/Δx

• y2-y1/x2-x1

• m

• the average rate of change

the tangent line is

• a line that hits 2 points (average rate of change)

• a line that hits one point

• one point on the graph, you need to use limits to solve

a secant line is

• a line that hits one point

• a line that hits 2 points (average rate of change)

• one point on the graph, need to use limits for

formula for average rate of change:

• f(x+h)-f(x)/(x+h)-x

• y2-y1/x2-x1

• f(x+h)-f(x)/h

• f(x)-f(a)/(x-a)

(x+h)^2 does not equal

the derivative is the

ways to write the derivative

• y' or f'(x)

• dy/dx or d/dx

• derx or dery

• Δy/Δx

equation of the tangent line

• y-y1=m(x-x1)

• y-y1=m(x+x1)

• y+y1=m(x-x1)

• y+y1=m(x+x1)

when given that f(3)=-1 and f'(3)=5 find and explain the equation for the tangent line

• tangent line = y+1=5(x+3) because f(3)=1 gives the y1 and x1, and then the 5 gives m

• tangent line = y-1=5(x-3) because f(-3)=-1 gives the y1 and x1, and then the 5 gives m

• tangent line = y+3=5(x+1) because f(-3)=-1 gives the y1 and x1, and then the 5 gives m

a derivative exists when the function is

• a smooth curve

• continuous

• without sharp turns

• with infinite tangents