EMC Q.28
0. 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
