BC

Question 1

Average Rate of Change

Answer 1

Slope of secant line between two points, use to estimate instantanous rate of change at a point.

Question 2

Instantenous Rate of Change

Answer 2

Slope of tangent line at a point, value of derivative at a point

Question 3

Formal definition of derivative

Answer 3

limit as h approaches 0 of [f(a+h)-f(a)]/h

Question 4

Alternate definition of derivative

Answer 4

limit as x approaches a of [f(x)-f(a)]/(x-a)

Question 5

When f ‘(x) is positive, f(x) is

Answer 5

increasing

Question 6

When f ‘(x) is negative, f(x) is

Answer 6

decreasing

Question 7

When f ‘(x) changes from negative to positive, f(x) has a

Answer 7

relative minimum

Question 8

When f ‘(x) changes fro positive to negative, f(x) has a

Answer 8

relative maximum

Question 9

When f ‘(x) is increasing, f(x) is

Answer 9

concave up

Question 10

When f ‘(x) is decreasing, f(x) is

Answer 10

concave down

Question 11

When f ‘(x) changes from increasing to decreasing or decreasing to increasing, f(x) has a

Answer 11

point of inflection

Question 12

When is a function not differentiable

Answer 12

corner, cusp, vertical tangent, discontinuity

Question 13

Product Rule

Answer 13

uv’ + vu’

Question 14

Quotient Rule

Answer 14

(uv’-vu’)/v²

Question 15

Chain Rule

Answer 15

f ‘(g(x)) g’(x)

Question 16

y = x cos(x), state rule used to find derivative

Answer 16

product rule

Question 17

y = ln(x)/x², state rule used to find derivative

Answer 17

quotient rule

Question 18

absolute value of velocity

Answer 18

speed

Question 19

y = sin(x), y’ =

Answer 19

y’ = cos(x)

Question 20

y = cos(x), y’ =

Answer 20

y’ = -sin(x)

Question 21

y = tan(x), y’ =

Answer 21

y’ = sec²(x)

Question 22

y = csc(x), y’ =

Answer 22

y’ = -csc(x)cot(x)

Question 23

y = sec(x), y’ =

Answer 23

y’ = sec(x)tan(x)

Question 24

y = cot(x), y’ =

Answer 24

y’ = -csc²(x)

Question 25

y = sin⁻¹(x), y' =

Answer 25

y' = 1/√(1 - x²)

Question 26

y = cos⁻¹(x), y' =

Answer 26

y' = -1/√(1 - x²)

Question 27

y = tan⁻¹(x), y' =

Answer 27

y' = 1/(1 + x²)

Question 28

y = cot⁻¹(x), y' =

Answer 28

y' = -1/(1 + x²)

Question 29

y = e^x, y' =

Answer 29

y' = e^x

Question 30

y = a^x, y' =

Answer 30

y' = a^x ln(a)

Question 31

y = ln(x), y' =

Answer 31

y' = 1/x

Question 32

y = log (base a) x, y' =

Answer 32

y' = 1/(x lna)

Question 33

To find absolute maximum on closed interval [a, b], you must consider...

Answer 33

critical points and endpoints

Question 34

mean value theorem

Answer 34

if f(x) is continuous and differentiable, slope of tangent line equals slope of secant line at least once in the interval (a, b) f '(c) = [f(b) - f(a)]/(b - a)

Question 35

If f '(x) = 0 and f"(x) > 0,

Answer 35

f(x) has a relative minimum

Question 36

If f '(x) = 0 and f"(x)

Answer 36

f(x) has a relative maximum

Question 37

Linearization

Answer 37

use tangent line to approximate values of the function

Question 38

rate

Answer 38

derivative

Question 39

left riemann sum

Answer 39

use rectangles with left-endpoints to evaluate integral (estimate area)

Question 40

right riemann sum

Answer 40

use rectangles with right-endpoints to evaluate integrals (estimate area)

Question 41

trapezoidal rule

Answer 41

use trapezoids to evaluate integrals (estimate area)

Question 42

Intermediate Value Theorem

Answer 42

If f(1)=-4 and f(6)=9, then there must be a x-value between 1 and 6 where f crosses the x-axis.