Math Test 3

Question 0

A tangent line is

Answer 0

Only touches a point of a curve, locally speaking

Question 1

A secant is

Answer 1

A line connecting two points of a curve

Question 2

How to find the slope of a secant line

Answer 2

(Y2-y1/x2-x1) like all slopes

Question 3

How to find slope of tangent line

Answer 3

Find the derivative of the secant’s slope or use the formula (f(x)-f(a))/(x-a)
See page 52 for details

Question 4

Derivitative at a point

Answer 4

F’(a)=f(x) -f(a)/x - a

Question 5

Derivitave at a whole funciton

Answer 5

Limit as h approaches zero is
F’(x)=f(x+h) -f(x)/h

*always plug in 0 for h

Question 6

True or false: d/dx =f’(x)

Answer 6

True

Question 7

Power rule of derivativex

Answer 7

F’(x^n) = nx^(n-1)

Note:sqrt(x) = x^(1/2) and ^d sqrt(x^n) =x^(n/d)
See pg54

Only applicable when:

• base is just x (not 5x+5 par example)
• the exponent is a contstant (not ^5x)
• the base is x and the expnent is a constant (not 4^x)

Question 8

Steps for finding derivative in calculator

Answer 8

F3, open parenthesis, then (whatever the function is), comma, x, close parenthesis

Question 9

What is the derivative of a constant?

Answer 9

Zero. Always
Example: f'(x)=7
7-7/h
7-7/0
0/0

Question 10

Derivative formula 1

D/dx(k*f(x))=

Answer 10

K*d/dx((f(x))

Question 11

Derivatvie rule:

D/dx(f(x)+g(x))=

Answer 11

D/dx(f(x)+d/dx(g(x))

Question 12

Derivtive rule

D/dx(f(x)-g(x))

Answer 12

=d/dx(f(x)-d/dx(g(x))

Question 13

Limit rule

Lim(k*f(x))=

Answer 13

K*lim(f(x))

Question 14

Lim(f(x)+g(x))

Answer 14

=lim(f(x)+lim(g(x))

Question 15

Limit rule

D/dx(f(x)-g(x)=

Answer 15

D/dx(f(x)-d/dx(g(x)

Question 16

The product rule for limits

Answer 16

Lim(f(x)g(x)) =lim(f(x))lim(g(x))

Question 17

True or false: the derivative of a product is the product of its derivatives

Answer 17

False. The product rule for limits is not the same as the product rule for derivatives

Question 18

The product rule of derivatives

Answer 18

D/dx(f(x)g(x))=d/dx(f(x))g(x)+f(x)*d/dx(g(x))

Question 19

The quotient rule (of derivatives)

Answer 19

Derivative of (f(x)/g(x))=((derivative of f(x))*g(x) - f(x) *(derivate of g(x)))/ (g(x))^2

Or
(F/g)’=(f’g-fg’)/g^2

Question 20

When do you use chain rule?

Answer 20

Since you cant use the power rule to differentiate lets say (2x+4)^3, you have to use the chain rule instead.

Question 21

Chain rule

Answer 21

Derivative of ((g(x)^n))=n*g(x)^(n-1) * g’(x)

Bsically power rule times derivative