"This Is What You Think Of Doing"

Question 1

Find the equation of the line tangent to f(x) on (a,b)

Answer 1

Take derivative which is the slope, and use point slope form

Question 2

Find the equation of like normal to f(x) on (a,b)

Answer 2

Find the slope(take derivative and plug in point) but slope is -1/f’(x)

Question 3

Show that f(x) is even

Answer 3

Show that f(-x)=f(x) is symmetric to the y-axis

Question 4

Show that f(x) is odd

Answer 4

Show that f(-x)=-f(x) is symmetric to the origin

Question 5

Find the interval where f(x) is increasing

Answer 5

Find f’(x), set numerator/denominator equal to zero to find critical points, make sign chart, where it is positive

Question 6

Find the interval where the slope of f(x) is increasing

Answer 6

Take the f’‘(x) set both numerator/denominator to zero make sign chart for f’’ and determine where it is positive

Question 7

Find the minimum vale of a function

Answer 7

Make sign chart of f’(x), fund relative minimums and plug into f(x) choose the smallest

Question 8

Find the minimum SLOPE of a function

Answer 8

Find f’’, find relative mins, plug into f’ and choose the smallest

Question 9

Find the critical values

Answer 9

Find f’ and set equal to zero

Question 10

Find inflection points

Answer 10

Find f’’ set equal to zero make sign chart, look for sign changes

Question 11

Show that Lim x–>a f(x) exists

Answer 11

Show that the left hand and right hand limits equal each other

Question 12

Show that f(x) is continuous

Answer 12

1. Show that the limit exists
2. F(a) exists
3. The limit=f(a)

Question 13

Find the vertical asymptote a if f(x)

Answer 13

Factor and cancel what you can, set denominator equal to 0

Question 14

Find the horizontal asymptotes of f(x)

Answer 14

Find the left and right hand limits of f(x)

Question 15

Find the average rate of change

Answer 15

b-a

Question 16

Find the instantaneous rate of change of f(x) at a

Answer 16

f’(a)

Question 17

Find the average value

Answer 17

1/b-a time the integral of f(x) dx

Question 18

Find the absolute max of f(x) on (a,b)

Answer 18

Find f’, make a sign chart, find relative maxs, plug back into f(x) as well as finding f(a) and f(b) and choose the LARGEST

Question 19

Show that the piece wise function is differentiable

Answer 19

Show that the limit from

Question 20

Given position find velocity

Answer 20

V(t)=s’(t)

Question 21

Given v(t) find how far the particle travels

Answer 21

Integral from a to b of |v(t)| ft

Question 22

Find the average velocity of a particle

Answer 22

b-a

Question 23

Given v(t) determine if a particle is speeding up @ t=k

Answer 23

Find v(k) and a(k) and multiply their signs, if both are positive it is speeding up if different then the particle is slowing down

Question 24

Given v(t) and s(0) find s(t)

Answer 24

s(t)= the integral a of v(t) dt + C; plug in t=0 to find C

Question 25

Show that Rolle's Theorem holds on (a,b)

Answer 25

Show that f is continuous and differentiable on the interval; if f(a)=f(b) find f'(c)=0

Question 26

Show that mean value theorem holds on (a,b)

Answer 26

f'(c)= f(b)-f(a) -------- b-a

Question 27

Find the domain of f(x)

Answer 27

Assume domain is (-infinity,infinity) with restrictable domains

Question 28

Find range of f(x)

Answer 28

Use min/max techniques to find relative min:Mac the examine the lim of f(x)

Question 29

Find f'(x) by definition

Answer 29

Lim h-->0 f(x+H) -f(x)/h Or Lim x--> f(x)-f(a)/x-a

Question 30

Find the inverse to f(x) at x=a

Answer 30

Find the Decatur implicitly plug the x value into the inverse relation and solve for y. Find y into the derivative

Question 31

Y is increasing proportionally to y

Answer 31

Y=Pe^rt

Question 32

Find the area under the curve

Answer 32

Integral from a to c= integral from c to b

Question 33

Derivative of integral from a to x of f(t) dt

Answer 33

F(x)

Question 34

Derivative of the integral if f(t) from a to u

Answer 34

f(u) times u'

Question 35

The rate of change if population is

Answer 35

dP --- = ... dt

Question 36

The line y=mx+b is tangent to f(x) at (X1,y1)

Answer 36

They share the same slope f' and the same y value at x1

Question 37

Find the area using left Riemann sum

Answer 37

A= base time x0+x1+xn-1

Question 38

Find area using right Riemann sum

Answer 38

A=base times X1+x2+....

Question 39

Find area using midpoint rectangles

Answer 39

Usually with a table, if you are given 6 sets of points only do 3 rectangles

Question 40

Find area using trapezoids

Answer 40

A=base/2 times (x0+2x1+.....xn)

Question 41

Solve the differentiable equation

Answer 41

Separate the variables, solve for y

Question 42

Meaning of integral of f(t) dt from a to x

Answer 42

Area under the curve from a to x

Question 43

Given a base, cross sections perpendicular to the x-axis are squares

Answer 43

Volume= integral from a to b, of base squared dx

Question 44

Find where the tangent line to f(x) is horizontal

Answer 44

Find f' set the numerator equal to zero

Question 45

Find where the tangent line is vertical

Answer 45

Find f' set the denominator equal to 0

Question 46

Find the minimum acceleration given v(t)

Answer 46

Find a(t)=v'(t) the find a'(t)

Question 47

Given the value of f(a) and the fact that the anti-derivative of f is F, find F(b)

Answer 47

find the integral of F(x) on (a,b)!solve for F(b)

Question 48

Find the derivative of f(g(x))

Answer 48

Chain rule | F'(g(x)) times g'(x)

Question 49

Find the zeros

Answer 49

Set equal to zero, factor/quadratic equation; graph to find zeros on calculator