Question

2 between x x2 Determine the average rate of change of f(x) 1 and x 1+h. Simplify your answer completely. Average rate of change: Consider the graph of the line Cx + Ay = B where A, B, and C are all positive constants. If the value of B is doubled, what happens to the slope of the line? Be specific and give your reason.

Answer 1

f(x) = 2/x^2

between x = 1 , x = 1+ h

average rate of change = f(b) - f(a) / ( b - a )

f(1 +h) = 2 / ( 1+ h)^2

= 2 / ( 1 + h^2 + 2h )

f(1) = 2 / 1^2 = 2

f(1+h) - f(1) / ( 1 + h -1 )

= ( 2 / ( 1 + h^2 + 2h ) - 2 ) / h

= ( 2 - 2 - 2h^2 - 4h ) / ( 1 + h^2 + 2h ) / h

= ( - 2h^2 - 4h ) / h ( 1 + h^2 + 2h )

average rate of change = ( - 2h^2 - 4h ) / ( h^3 + 2h^2 + h )

2)

Cx + Ay = B

y = - C/A x + B

slope of this line is

- C/A

so if we increase the value of B

there will be no effect on the slope

slope remains same