Chapter 2.1, Problem 1C

(a)

To determine

Whether given statement is true or false.

‘The slope of the tangent line to the function $f(x)$ at the point $x=4$ is given by $f\text{'}(4)$ ’

(b)

To determine

Whether given statement is true or false.

‘The instantaneous rate of change of a function $f(x)$ at the point $x=-3$ is given by $f\text{'}(-3)$’

(c)

To determine

Whether given statement is true or false.

‘The instantaneous rate of change of a function $f(x)$ at the point $x=a$ cab be represented as a slope of the secant line’

(d)

To determine

Whether given statement is true or false.

‘Where a $f(x)$ is positive, its associated slope function $f\text{'}(x)$ is increasing.’

(e)

To determine

Whether given statement is true or false.

‘Where a $f(x)$ is decreasing’, its associated slope function $f\text{'}(x)$ is negative’

(f)

To determine

Whether given statement is true or false.

‘When a function $f(x)$ has steep slope at a point on its graph its instantaneous rate of change at that point will have a large magnitude’

(g)

To determine

Whether given statement is true or false.

‘When the graph of function $f(x)$ is decreasing with steep slope the graph of the associated slope function $f\text{'}(x)$ is negative with large magnitude’

(h)

To determine

Whether given statement is true or false.

‘Suppose an object is moving in a straight path with position function $s(t)$ .If $s(t)$ is positive and decreasing, then the velocity $v(t)$ is negative.’