Calc 2

average rate of change

Slope of secant line over an interval\

Delta H (t)/delta t

instantaneous rate of change

slop of tangent line at a point

F’(x)

Dy/dx

Limit of difference quotient:

Delta H (t)/ delta t

Lim delta t —>0

(Also known as derivative)

instantaneous rate of change at x=a (h→0)

Lim h—>0 f(a+h)-f(a)/h (THIS GIVES A NUMBER)

Lim h→0 f(x+h)-f(x)/h=f’(x) (THIS IS A FUNCTION)

When to use function equation vs number equation

function: asking to find the derivative of a equation and the instaneous rate of change at multiple x point

Number: Asia’s to find instantaneous rate of change at one x point

instananeous rate of change at x=a (x→a)

lim x—>a f(x)-f(a)/x-a

AROC over interval [a, ah]

F(a+h)-f(a)/h

(No limit statement)

AROC over interval [a, x]

f(x)-f(a)/x-a

Find the equation of the line tangent to the graph of ___

find derivative at the point, then use point slope formula

Y—y1=m(x-x1) or y-f(a)=f’(a) (x-a)

Ways to write derivative