section 2.1 and 2.2 the tangent and velocity problems

What is a tangent line to a curve

A line that touches the curve at a point and has the same slope / direction as the curve at that point

How do your approximate the slope of a tangent line

Use a secant line through P(a, f(a) and Q(x, f(x))

MPQ= f(x)-F(a)/ x-a

How do you find the exact slope of a tangent line

Take the limit of the slopes of secant lines

M

M = limx→a f(x) -f(a) / x-a

Find the slope of the tangent line to y =x² at (1,1)

M = limx→ 1 x²-1/x-1 = 2

Equation of the tangent line to y=x² at (1,1)

Y = 2x-1

What does the slope of a position time graph represent

Instaneous velocity

Formula for instanteous velocity at T=a

V = lim h→0 s(a+h) -s(a) / h

How is average velocity over [T1, T2] defined

S(t2) - s(t1) / t2-t1

What does a negative slope mean in physical problems

The quantity is decreasing

What is an infinite likit