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# Polynomial Functions Review

Published on: Mar 4, 2016
Published in: Education      Technology      Entertainment & Humor

#### Transcripts - Polynomial Functions Review

• 1. Unit 2 Review Composite Functions, Derivative, Polynomials
• 2. Composite Functions <ul><li>Find f[g(0)]. </li></ul><ul><li>Given: </li></ul><ul><li>Find an equation for: </li></ul>
• 3. The Derivative & Its Applications <ul><ul><li>Remember that ‘the derivative’ of a function is another name for the slope, or rate of change of that function. It is also known as the ‘slope of the tangent line’ and ‘instantaneous rate of change.’ </li></ul></ul><ul><ul><li>Ex: Prove, using the “definition of a derivative” that the derivative of is </li></ul></ul>
• 4. The Derivative & Its Applications <ul><ul><li>Ex: Find the equation of the tangent line of y=2x 3 -1 at x=2. </li></ul></ul><ul><ul><li>Solution: </li></ul></ul><ul><ul><li>First, we need to find the slope of this tangent line – the derivative of the function, when x=2. </li></ul></ul><ul><ul><li>The next thing we need to do is find the y-coordinate of our original function when x=2. </li></ul></ul><ul><ul><li>Then we come up with our equation of the line: </li></ul></ul>
• 5. Polynomial Functions <ul><li>Consider the following function: </li></ul><ul><li>Find the y-intercept. </li></ul><ul><li>Find the x-intercept(s). </li></ul><ul><li>Find the critical points and state whether each is a min. or max. </li></ul><ul><li>Find the intervals of increase and decrease. </li></ul><ul><li>Sketch the function. </li></ul>
• 6. Polynomial Functions <ul><li>Consider the following function: </li></ul><ul><li>Find the y-intercept. </li></ul><ul><li>Find the x-intercept(s) – use either long division or synthetic substitution. </li></ul><ul><li>Find the critical points and state whether each is a min. or max – find the derivative; set it equal to zero; solve for x. </li></ul><ul><li>Max or min? Plug into original function. </li></ul>
• 7. Polynomial Functions <ul><li>Intervals of increase/decrease. </li></ul><ul><li>Test value: 0 – check y ′ . </li></ul><ul><li>f(x) is increasing on x  (-  ,2.74)  (5.52,  ) </li></ul><ul><li>f(x) is decreasing on x  (2.74, 5.52) </li></ul><ul><li>5. Sketch the graph. </li></ul>