Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Calculus

Question:

If x is real, the minimum value of $f(x)=x^2-8x+20 $ is :

Options:

4

1

2

3

Correct Answer:

4

Explanation:

The correct answer is Option (1) → 4

$f(x)=x^2-8x+20$

$f(x)=(x^2-8x+16)+4=(x-4)^2+4$

$(x-4)^2≥0$

Since $(x-4)^2≥0\,∀\,x$, minimum value $(x-4)^2=0$, i.e. at $x=4$

$f(4)=0+4=4$