1. This document is a final exam for a bilingual high school differential calculus course. It consists of 10 multiple choice and free response questions testing concepts like limits, derivatives, optimization, and graph sketching. 2. The exam is worth a total of 100 points and will be graded based on various components like exams, homework, quizzes and class activities. Partial credit is given for showing work even if the final answer is incorrect. 3. Questions cover topics like finding the domain and range of functions, limits, derivatives using definitions and rules, implicit differentiation, optimization, related rates, and graph sketching through identifying key features.

1. BILINGUAL HIGH SCHOOL
DIFFERENTIAL CALCULUS
COURSE
FINAL EXAM
EXAM EVALUATION POLITICS : AVERAGE GRADE 60%
If you write only the answer = 0% of the value EXAM 30% __ _____
If you write a wrong answer with the correct CLASS ACTIVITIES 4% ____________
procedure = 75% HOMEWORKS 3% ____________
To have the 100% of the grade you must QUIZ 1% ____________
include correct procedure and correct answer. REVIEW 2% ____________
TOTAL __________
Name: ______ID: ________
Date:___________________________________________
1. ( 1 point each ) For the following functions, determine domain and range, sketch the graph and
identify the shape ( do not use t-charts):
x2 5x 6
a). f x b) gt 1 x3
x 2
2. ( 1point each one) Find the limit if it exists by using the appropriate techniques.
x 4 if x > 4 lim x 9
x 9
f(x)=
8 –2x if x< 4
find lim f ( x)
x 4

2. 3.- (2 points) Given the function:
Give the limit definition of the derivative.
Find the derivative by using the limit definition.
Check your result by using the appropriate differentiation formula
1
f ( x)
x2
4. (1 point each one ) Find the first derivative of the following functions by using the appropriate
differentiation rules.
3x 2
a) f ( x) tan(cos x) b) f ( x)
7x 3
4
2 t cos t y 6
c) g (t ) t e d) f ( y )
y 7
4
(6 x 2 5)
e) f ( x)
8 x3
5. ( 1 point ) Find y´given the following equations, by implicit differentiation ( remember to get
dy
). cos(x y) y 2 cos x
dx

3. 6. (1 points ) Find the 3rd derivative of the following function:
4
y sin 3x 2x 3
x2
7. ( 4.5 points ) The Hubble Space Telescope was deployed on April 24, 1990, by the space
shuttle Discovery. A model for the velocity of the shuttle during this mission, from liftoff
at t=0 until the solid rocket boosters were jettisoned at t = 126 sec is given by
v(t)=0.001t3 –0.1t2 +24t – 3 in feet per second. Using this model, determine the maximum
and minimum values of the acceleration of the shuttle between liftoff and the jettisoning of
the boosters.
deploy: desplegado shuttle: lanzador
liftoff: despegue vertical jettisoned: desacoplamiento
8. ( 4.5 points ) Air is pumped into a shperical ballon so that ts volume increases at a rate
of 100 cm3/sec How fast is the radius of the ballon increasing when de diameter is 50 cm?
4 3
Remember volume of sphere: V r
3
9. ( 4 points) If 1200cm2 of material is available to make a box with a square base and an
open top, find the largest possible volume of the box..
10. ( 4 points ) Sketch the graph of the function by completely the 10 steps
10 STEPS (you may also use 8 steps if you prefer)
1. - Domain 6. - Extreme point (Maxima and minima of functions)
2. - Symmetry 7. - I.D.Test
3. - x intercept and y intercept 8. - Point of inflection
4. - Vertical Asymptotes 9. - Concavity
5. - Horizontal Asymptotes 10. - Sketch the graph(no t-charts)
x
ƒ(x) =
(x 2) 2