Unit 9 Math Test

Question 1

Derivative of a constant function

Answer 1

0

Question 2

Power Rule

Answer 2

n * x^n-1

Question 3

Sum and Difference Rule

Answer 3

f’(x) + g’(x)

Question 4

Product Rule

Answer 4

f’(x)g(x) + f(x)g’(x)

Question 5

Quotient Rule

Answer 5

(Low di Hi - Hi di Low)/Low^2

Question 6

Chain Rule

Answer 6

O’(I) * I’

Question 7

Second Derivative

Answer 7

y^n

Question 8

Third Derivative

Answer 8

y^m

Question 9

f(x) = b^x

Answer 9

f’(x) = b^x * ln(b)

Question 10

f(x) = e^x

Answer 10

f’(x) = e^x

Question 11

f(x) = logb(x)

Answer 11

f’(x) = 1/(xln(b))

Question 12

What is a derivative?

Answer 12

An instantaneous rate of change. The slope of the tangent line.

Question 13

Slope of the Secant Line

Answer 13

Slope formula

Question 14

“Find the instantaneous rate of change”

Answer 14

lim Q->p f(x2) - f(x1)/ x2-x1

Question 15

“Write the equation of the line tangent to”

Answer 15

Point-slope form
y - y1 = m(x - x1)

Question 16

Definition of Derivative (equation)

Answer 16

f’(x) = lim -> 0 f(x+h) - f(x) / h

Question 17

If you’re finding a derivative from a point

Answer 17

DON’T USE THE H DEFINITION

Question 18

When is a point differentiable?

Answer 18

A point (a, f(a)) is differentiable if it has a derivative at x = a

Question 19

Name the four cases where a function is not differentiable

Answer 19

1. Corner: f(x) = |x| at x = 0
2. Cusp: f(x) = x^2/3 at x = 0
3. Vertical Tangent: f(x) = cubed(x) at x = 0
4. Discontinuity

Question 20

What is the relationship between differentiable and continuous functions?

Answer 20

is f(x) is differentiable at x = a then it is continuous at x = a

Question 21

f(x) = ln(x)

Answer 21

f’(x) = 1/x

Question 22

d/dx[f^-1(x)]

Answer 22

1/f’(f^-1(x))