Use your birthday to create a functionf(x) = x³ + (Month) · x² – (Day) · x+ (Year).Find any inflection points for your function. Tell where this function is concave up andwhere it is concave down. Show how you decide this.

Answered: Use your birthday to create a function…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Use your birthday to create a function
f(x) = x³ + (Month) · x² – (Day) · x+ (Year).
Find any inflection points for your function. Tell where this function is concave up and
where it is concave down. Show how you decide this.

Expert Solution

Step 1

$\begin{array}{l} We have \\ f (x) = x^{3} + (Month) x^{2} - (Day) x + y e a r \end{array}$

Step 2

$\begin{array}{l} Now \\ f (x) = x^{3} + 3 x^{2} - 12 x + 1993 \\ Differentiate w.r.t "x" \\ f' (x) = 3 x^{2} + 6 x - 12 \\ Differentiate w.r.t "x" \\ f'' (x) = 6 x + 6 \\ Put f'' (x) = 0 \\ 6 x + 6 = 0 \\ 6 (x + 1) = 0 \\ x = - 1 \\ This is the only inflection point. \\ Now Domain of function is (- \infty, \infty) \\ Combine the inflection point with domain we get the intervals. \\ - \infty < x < - 1, - 1 < x < \infty \end{array}$