Calculus Review. How do I know where f is increasing? O It is where f prime is positive. O Find the...
-
Upload
megan-powers -
Category
Documents
-
view
215 -
download
0
Transcript of Calculus Review. How do I know where f is increasing? O It is where f prime is positive. O Find the...
Calculus Review
How do I know where f is increasing?
O It is where f prime is positive.O Find the derivative and set equal to
zero. Use test points to find where f prime is positive or negative.
How do I know where f has inflection points?
O It is where f double prime equals zero or is undefined and the sign changes.
O The f prime function changes from increasing to decreasing or vise-versa.
O It is where f prime has maximums or minimums.
How do I know if the particle is moving to the left?
O It is where f prime is negative.O Find where f prime equals zero.
Then check test points on f prime.
How do I know if the particle is speeding up or
slowing down?
O Find v(t) and a(t): If they have the same sign the particle is speeding up.
O If they have different signs the particle is slowing down.
What is speed?
OIt is the absolute value of velocity.
What do I do if the problem says find the particular
solution y = f(x)?
O This is asking you to find the original function that represents f. You are probably doing a separable variable problem.
What does mean?
OThis is asking for the first derivative.
OIt could also be written
What does mean?O This is asking for the second
derivative.O It could also be written .
What is the limit definition of a derivative?
OOr
What are the limit rules?
O Is it a hidden derivative?O If it’s approaching infinity and it’s a
polynomial over a polynomial then use the horizontal asymptote rules.
O Can you factor to simplify and just plug in the numbers.
How do I prove a function is continuous?
Show the left hand limit and the right hand limit are equal and are equal to f(x).
Day One Practice
Differentiate: arctan 2x
21+4 𝑥 ²
Differentiate:
-
3×23𝑥×ln (2)
Differentiate:
,Find
−2 𝑥 (𝑥2+1 )− 2
, find
(𝑥2+1 )3 (9𝑥2−8 𝑥+1 )
∫ (sin (2𝑥 )+cos (3 𝑥 ) )𝑑𝑥=¿ ¿ + C
∫ 𝑥𝑥2−6
dx=¿
ln ⃒
. Find the x-coordinate(s) for points
of inflection on f.
x=4 and x=8
cos(xy)=x, find
−csc (𝑥𝑦 )− 𝑦𝑥
Find the slope of the line tangent to the curve y=arctan(3x) at x = .
32
Day Two Practice
Use a right Riemann sum with the four subintervals indicated by the data in the table to approximate
t (minutes) 0 5 9 12 20
W(t) degrees F
54.0 58.2 63.1 68.1 70
= 65.385
Is the previous estimate an overestimate or an
underestimate?
OIt is an overestimate, because the function is always increasing and the right Riemann sum would be above the curve.
, find .
𝑑𝑦𝑑𝑥
=− sin (𝑥 )+2 𝑦−10𝑥
−2𝑥
Find the solution y = f(x) to the given differential
equation with the initial condition f(-1) = 2.
𝑦=4
𝑥2+1
Write an equation for the line tangent to the graph of f
at x = -1 if f(-1)=2.
y – 2 = 2(x + 1)
Day Three Practice
∫ sin (3𝑥 )𝑑𝑥=¿−cos (3 𝑥)
3+𝐶
lim𝑥→ 0
2𝑥4+5𝑥3
5𝑥4+3 𝑥3
53
The function f is defined above. For what value of k, if any is f continuous at
x = 2?
k = -1
The function f given by has a relative
maximum at x = ?
X=0Where are the minimums?
X=-1.5 and x = 6
What is the slope of the line tangent to the
graph of
−5
16𝑒𝑥
=
𝑒3
=
43
𝑑𝑦𝑑𝑥∫0
𝑥2
sin (√2 𝑡 )𝑑𝑡=¿¿
2 𝑥(𝑠𝑖𝑛√2 𝑥2)