Exam 2

Question 1

f’(x)=sin(x)+cos(x) and g’(x)=sin(x)+cos(x) then

Answer 1

the equation of the tangent line at x will be the same for f(x) and g(x)

Question 2

the expression f(6+h)-f(6)/h represents

Answer 2

The slope of the secant line through the graph of a function

through two points, (a,f(a)) and (a+h, f(a+h))

Question 3

the expression lim/h->0 f(6+h)-f(6)/h represents

Answer 3

the slope of the tangent line to the graph of the function at x=a

Question 4

The function f(x)=x|x|

Answer 4

is continuous at x=0

is differentiable at x=0

Question 5

Absolute extrema can only occur at:

Answer 5

Critical points and end points.

Question 6

The derivative of position is…

Answer 6

velocity

Question 7

the derivative of velocity is…

Answer 7

acceleration

Question 8

the second derivative of position is…

Answer 8

acceleration

Question 9

The IROC can be represented graphically as…

Answer 9

the SLOPE of the tangent line

Question 10

The AROC can be represented graphically as…

Answer 10

the SLOPE of the secant line

Question 11

Sin(0)

Answer 11

0

Question 12

Cos(0)

Answer 12

1

Question 13

Sin(π)

Answer 13

0

Question 14

Cos(π)

Answer 14

-1

Question 15

Tan(0)

Answer 15

0

Question 16

Tan(π)

Answer 16

0

Question 17

Sin(π/2)

Answer 17

1

Question 18

Cos(π/2)

Answer 18

0

Question 19

Tan(π/2)

Answer 19

DNE

Question 20

When is a function not differentiable

Answer 20

corner, cusp, vertical tangent line, discontinuity

Question 21

Differentiability implies…

Answer 21

continuity, but not the other way around

Question 22

if f’(x) is positive then f(x) is…

Answer 22

increasing (positive slope)

Question 23

if f’(x) is negative then f(x) is…

Answer 23

decreasing (negative slope)

Question 24

if f’(a) = 0

Answer 24

• zero slope (function is just chillin)

- The function isn’t increasing or decreasing.

Question 25

The *equation* of a line needs two things

Answer 25

1) point (x1, y1) | 2) M=(slope/derivative)

Question 26

point slope form

Answer 26

y − y1 = m(x − x1)

Question 27

f(c) ≥ f(x) for all x | this output value is bigger than or equal to all other output values

Answer 27

f(c) is an absolute Max if

Question 28

f(c) is an absolute Min if

Answer 28

f(c) ≤ f(x) for all x | this output value is smaller than or equal to all other output values

Question 29

critical point

Answer 29

derivative is zero or undefined

Question 30

MVT

Answer 30

if f(x) is continuous on the closed interval [a,b], and differentiable on the open interval (a,b). Then there exists a value c on the interval (a,b).

Question 31

MVT equation

Answer 31

f(b)-f(a)/b-a