Question

# Consider the function *f*(*x*) = *x*^{2} - *x*. Compute the average rate

of change of *f* as *x* varies from 1 to 1 + *h*. Suppose now that *h* is a number that is close to zero, but is slightly larger than 0 or slightly smaller than 0. The average rate of change of *f* as *x* varies from 1 to 1 + *h* is the slope of the line that is passing through the points (1, *f*(1)) and (1+*h*, *f*(1+*h*)). Imagine that the first point is fixed, but that the second point is a point on the curve that is moving towards the first.

The graph above shows the function along with two secant lines, one with *h*=1 and another with *h*=0.5 and the tangent line. Note how the slopes on the secant lines approach the slope of the tangent line as *h* approaches zero. Answer the following questions:

#### Top Answer

Answer: 1. Average rate of change of f as x varies from 1 to 1 + h: =>1+h 2. specific values for the average... View the full answer