2.1-2.4

Question 1

tangent line

Answer 1

a line following the shape of the curve at a point
does not necessarily hit f(x) again

Question 2

secant line

Answer 2

a line that can intersect a curve at LEAST twice

Question 3

slope of secant line

Answer 3

f(x)-f(c)/x-c

Question 4

slope of tan

Answer 4

lim x–> c f(x)-f(c)/x-c
where c is the point in question

Question 5

f’(c)=

Answer 5

slope of tan line, derivative

Question 6

derivative w/o point

Answer 6

f’(x)= lim h–> 0 f(x+h)-f(x)/h

Question 7

h =

Answer 7

delta x

Question 7

vertical tangent

Answer 7

lim = +/- inf (DNE)
number lim approaching is vertical tan

Question 8

derivatives that fail to exist

Answer 8

corners, cusps, vertical tangents, where not continuous

Question 9

to be differentiable a function…

Answer 9

• must be continuous
• lim h–>0 f(x+h)-f(x)/h must exist

Question 10

theorem: differentiability implies continuity

Answer 10

if a function is differentiable at x=c, it is continuous at x=c

Question 11

if f’(c) exists, equation of tan line=

Answer 11

y-f(c)=f’(c)(x-c)