Chapter 6.8, Problem 33SGR

To determine

To calculate: The number of turning points the graph joined by the point $\left(1,675\right),\left(2,950\right),\left(3,550\right),\left(4,250\right),\left(5,600\right),\left(6,400\right)$ have.

Answer to Problem 33SGR

The graph has three turning points.

Explanation of Solution

Given information:

The six points $\left(1,675\right),\left(2,950\right),\left(3,550\right),\left(4,250\right),\left(5,600\right),\left(6,400\right)$ .

Calculation:

Consider the six points $\left(1,675\right),\left(2,950\right),\left(3,550\right),\left(4,250\right),\left(5,600\right),\left(6,400\right)$ . Plot these points and connect these to obtain a polynomial function graph.

  

The function has relative high and low values of function. A function has relative minimum when no other near by point has a lesser y -coordinate. A function has relative maximum when no other near by point has a greater y -coordinate.

The graph has three turning points that is its value changes from high to lowest and then again high.

Observe from the graph that the polynomial function has the value greater than the surrounding points at $x=2\text{ and }x=5$ , so there must be a relative maximum at this point.

Similarly, the polynomial function has the value less than the surrounding points at $x=4$ , so there must be a relative minimum at this point.