**Unformatted text preview: **.8 9 24) Given the following graph of function, g(x), 3 3 PM
53%
a) Find all x values where the graph is discontinuous.
b) For each discontinuous x value, name the type of discontinuity.
c) For each discontinuous x value, state why it fails the formal definition of continuity.
d) Determine the intervals where the function is continuous.
6 of 7
a) X= -4, -3, -2 34
d(-co,-4)
5) point / loritovablo -> x=-4, 4
(-4,-3)v
(Infink -X=-3 3
(-3-25V
Jump->x=-2
(-2, 3)V
i ) Ha) DUE-,X--4 iu ta tami
(3, 4) 0
udi) LIMA DUE +X--3, -2,3
x=4
(4, 00)
6
25) Given: y = x2 - 5x + 9, find >. Show all work using the formal definition of the derivative.
he= lim f(kin ) -To>
h->0
-lim (x4h)?-s(xth) +q - (xisx +9)
h-70
u
um x taxt the sy-sita-242x A_Jim ax th -5
h-0
h
-ax-S
26) a) What is the equation of the tangent line at x = -3 for the function f (x) = 5x2 - 2x - 2?
$' (x )- 10x-a
y=$ (-3)= 51-3) -2(-3) -
m= $'(-3) = 10(-3)-2= -38
=49
y-49- -3a(x+3)
b) What is the slope of the normal line for f(x)?
1 slope
3a
27) The graph of f (x) is shown to the right.
a) Is f continuous at x = 0? Why or why not?
no, lim fu) + limf()
X -, 0
X-70*
b) Is f differentiable at x = 0? Why or why not?
no, be cause it isn't
Continuous
c) Using the domain of [-3, 3], state the x-intervals where f(x) is differentiable
(-3, 0Ju(D, 3)
7
28) Find the derivative of the following functions. State the formula used for each.
us
Rodud lol a) 3 = (x3 - 6x) (2 - 4x3)
Quohert
)y - 23+3
u'.v-u'v
u'.v+u.V
u= 3x2V V=-lax
N's 8x v'= 3x2
va
Sx 4+24 x - 12x 4
,-(8M(x 343)-(4x) (3x?)...

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- Fall '16
- Ms. Grieco
- Calculus, Derivative, Continuous function, X Values