Question

IV. Evaluating a Difference Quotient Read about the difference quotient (section 1.8 page 218). a) Provide a sketch of the function f(x) = -3x + 2. (3 pts.) b) State the difference quotient. (3 pts.) c) Find the difference quotient for this function and simplify. (3 pts.) d) Compare your result to the function. What do you think the difference quotient represents for this function? (3 pts.) e) Let k(x) = x - x. Find the average rate of change on [-2, 1]. Make sure you show all algebraic steps. Is the average rate of change increasing or decreasing? (section 1.4 page 157) (3 pts.)

please show each step and explain trying to learn for an upcoming test

Answer 1

f(x) = - 3x + 2

(0, 2) (0.667,0)

b)

difference quotient is

{ f(x+h) - f(x) } / h

c)

f(X) = - 3x + 2

f(x+h) = - 3(x+h) + 2

= - 3x - 3h + 2

difference quotient is

{ - 3x - 3h + 2 + 3x - 2 } / h

= -3h/h

= - 3

difference quotient = - 3

d)

difference quotient represents the slope or average rate of change of the function

e)

k(x) = x^2 - x

average rate of change on [ - 2, 1 ]

k(1) = 1^2 - 1 = 0

k(-2) = (-2)^2 - (-2) = 6

average rate of change = ( 0 - 6 ) / ( 1 - - 2 )

= - 2

average rate of change = - 2

average rate of change is decreasing