Question 1. Suppose that f is a function whose domain is R and satisfies the following properties: • f(x) = 0 when x < -1 • f(x) = 0 when x > 1 • f(0) = 1. 1. Define the function f on the interval [-1, 1] such that f is everywhere continuous. 2. Suppose that f must have the form of a quartic polynomial on [-1, 1]; that is, f(x) = c4x4+c3x³+c2x²+c1x+co. Find the values of co, ..., C4 such that f is everywhere differentiable. [-1, 1], and a point a e [-1,1]. Consider the triangle formed Question 2. Consider the function f(x) = 1 – x² on by the tangent line to f at a, and the lines x = 0 and y = 0. Find the points a such that the triangle has an area of exactly (1+ a?).

Question 1. Suppose that f is a function whose domain is R and satisfies the following properties: • f(x) = 0 when x < -1 • f(x) = 0 when x > 1 • f(0) = 1. 1. Define the function f on the interval [-1, 1] such that f is everywhere continuous. 2. Suppose that f must have the form of a quartic polynomial on [-1, 1]; that is, f(x) = c4x4+c3x³+c2x²+c1x+co. Find the values of co, ..., C4 such that f is everywhere differentiable. [-1, 1], and a point a e [-1,1]. Consider the triangle formed Question 2. Consider the function f(x) = 1 – x² on by the tangent line to f at a, and the lines x = 0 and y = 0. Find the points a such that the triangle has an area of exactly (1+ a?).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.1: Inverse Functions

Problem 56E

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