Ask Questions, Get Answers


Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=1-2x-x^{2}, [-4 , 1 ]$

Note: This is part 2nd of a 7 part question, split as 7 separate questions here.

1 Answer

  • To find the absolute maximum and minimum values of a continuous function f on a closed interval $[a,b]$
  • (i) Find the values of the critical numbers of f in $(a,b)$
  • (ii) Find the value of $f(a)$ and $f(b)$
  • (iii) The largest of the values from (i) and (ii) is the absolute maximun value, the smallest of these values is the absolute minimum value.
$f(x)=1-2x-x^2$ is continous on $[-4,1]$
Step 1:
$f'(x)=0=>x =-1$
Step 2:
The critical value of f is
The values of f at the endpoints are
Step 3:
Comparing the 3 values, the absolute maximum is $f(-1)=-1$ and the absolute minimum is $f(-4)=-7$
answered Jul 31, 2013 by meena.p

Related questions