Quiz 2

Question 1

Average speed

Answer 1

distance travelled / time taken

s(Tf) - s(T0) / tf - t0

f - end speed or time
0 - start speed or time

Question 2

Derivative equation

Answer 2

f’(x) = lim [ f(x+h) - f(x) ] / h

Question 3

3.1 derivatives

Answer 3

Find a common denominator and simplify

Question 4

Finding the derivative at a point

Answer 4

1. find the derivative of the function (m)
2. find the value of the y-coordinate by plugging the x-coordinate into the original function
3. substitute x and y coordinates and m into formula y - y₁ = m(x - x₁)

Question 5

Differentiation rules

Answer 5

1. constant rule
   k’ = 0 , derivative of a constant is zero
2. power rule
   xⁿ is nxⁿ⁻¹
3. sum rule
   ( f(x) + g(x) )’ = f’(x) + g’(x)
4. constant multiple rule
   ( k f(x) )’ = k f(x)’
5. higher order derivatives
   derivative of derivatives - f(x)’ 2nd order f”(x) 3rd order etc..

Question 6

Product differentiation rule

Answer 6

( f(x) * g(x) )’ = f’(x)g(x) + f(x)g’(x)

Question 7

Quotient differentiation rule

Answer 7

[ f’(x)g(x) - f(x)g’(x) ] / g(x)²