Solution Found!
Solved: Graphing polynomials Sketch a graph of the
Chapter 7, Problem 10E(choose chapter or problem)
9-14. Graphing polynomials Sketch a graph of the following polynomials. Identify local extrema, inflection points, and x- and y-intercepts when they exist.
\(f(x)=\frac{1}{15} x^{3}-x+1\)
Questions & Answers
QUESTION:
9-14. Graphing polynomials Sketch a graph of the following polynomials. Identify local extrema, inflection points, and x- and y-intercepts when they exist.
\(f(x)=\frac{1}{15} x^{3}-x+1\)
ANSWER:Solution: Step1 Given that f(x)=1/15 x^3-x+1 Differentiate the given equation to find f’(x) we get, f’(x)= 1/15*3*x^2 - 1 +0 = x^ -1 Again differentiate f’(x) to find f’’(x) we get, f’’(x)=2x/5-0=2x/5 Step2 To get extreme values we have to use f’(x)=0 => 3/15 x^2-1=0 =>3/15 x^2=1 => x^2= 1*15/3=5 => x=± 5 Critical points are - 5 and + 5 Step