Engineering Maths - Calculus
26. The minimum value of | x2-5x+21 | is
- Option : B
- Explanation :
Since the value of a mod function cannot be less than zero, therefore f(x) = | x2-5x+2 | is zero.
28. The maximum slope of the curve
-x3 + 6x2 + 2x + 1 is
- Option : A
- Explanation :
Let f(x) = -x3 + 6x2 + 2x + 1
Slope of the function is, f'(x) = -3x2 + 12x + 2 = F(x) (say) Now to find minimum or maximum of F(x) Therefore F'(x) = - 6x + 12 F"(2) = -6 For maxima and minima, F'(x) = 0 ⇒ x = 2Therefore F"(2) = -6Hence F(x) (slope) is maximum at x = 2Maximum slope = F(2) = -3(2)2 + 12(2) + 2 = 14
30. The function f(x) = x3 - 6x2 + 3x + 25 has
- Option : A
- Explanation : f ' (x) = 3(x2 - 4x + 3), f '' (x) = 6(x) - 12 At x = 1, f "(1) At x = 3, f " (3) = + ve
