Chapter 6.3, Problem 49PPS

To determine

To sketch:

The degree and the leading coefficient of the given graph.

Explanation of Solution

Given:

  $f\left(x\right)=x^4-3x^2+6x$

Concept used:

The leading coefficient is equal to the coefficient of the term with the highest exponent in the expression.

Calculation:

  $f\left(x\right)=x^4-3x^2+6x$

The degree is equal to the highest exponent in the expression.

The vertical tangent means that the derivative at that point approaches infinity.

Since the slope is infinitely large.

Test one point in each of the region formed by the graph.

If the point satisfies the function then shade the entire region to denote that every point in the region satisfies the function.

To draw a table

  $f\left(x\right)=x^4-3x^2+6x$

$x-axis$	$0$	$-2.33$	$-1.5$	$-2$
$y-axis$	$0$	$0$	$-10.73$	$-6$

To draw a graph