Consider function f(x)=1−2x2,−5≤x≤1. The absolute maximum value is and this occurs at x= The absolute minimum value is and this occurs at x=

Question

Consider function f(x)=1−2x2,−5≤x≤1.  The absolute maximum value is  and this occurs at x=  The absolute minimum value is  and this occurs at x=

Papilys3q · Accepted Answer

Step 1Consider the function f(x)=1−2x2,−5≤x≤1.Step 2Since the given function is a polynomial and so it  is continuous everywhere and therefore is continuous on the given interval.Now compute its first derivative and put it equal to zero to find its critical points f(x)=1−2x2f&#039;(x)=0-4xf&#039;(x)=-4xf&#039;(x)=0⇒−4x=0⇒x=0The critical point x=0 belong to the given interval.Step 3Now we find the function value at the critical points and the end points of the interval.f(x)=1−2x2f(−5)=1−2(−5)2=1-50f(-5)=-49f(0)=1−2(0)2f(0)=1f(1)=1−2(1)2f(1)=-1Absolute Maximum value is 1and this occurs at x=0.Absolute Minimum value is -49and this occurs at x=5.

Consider function f(x)=1-2x^{2}, -5\le x \le 1. The absolute maximum value

Answered question

Answer & Explanation

New Questions in Algebra I