Mathematics - Calculus
6. The minimum value of | x2 - 5x + 21 | is
- Option : B
- Explanation : Since value of a mod function cannot be less than zero, therefore f(x) = | x2 - 5x + 21 | is zero.
9. The function f(x) = 3x(x - 2) has a
- Option : A
- Explanation : f(x) = 3x (x - 2) = 3x2 - 6x
Differentiating, we get
Again diferentiating, 
For maxima or minima, - f '(x) =0
∴ 6x-6=0 ⇒ x=1
As f '(x) =6 >0 then f(x) is minimum at x=1
10. What is the derivative of f(x) = | x | at x = 0
- Option : D
- Explanation : f(x) = |x| and f(x) = x for x > 0 ⇒f(x) = -x for x < 0
Hence from the graph it is clear that derivative doesn't exists for x=0
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