QJEEM19Ma5085: JEE Main 2019 Mathematics - Class 12 JEEM19Ma5085 Solution: If S 1 and S 2 are respectively the sets of local minimum and…
If S1 and S2 are respectively the sets of local minimum and local maximum points of the function,
ƒ(x) = 9x4 + 12x3 – 36x2 + 25, x ∈ R, then :
Multiple Choice Options
AS1 = {–1}; S2 = {0, 2}
BS1 = {–2}; S2 = {0, 1}
CS1 = {–2, 0}; S2 = {1}
DS1 = {–2, 1}; S2 = {0}
Step-by-Step Verified Solution
ƒ(x) = 9x4 + 12x3 – 36x2 + 25
ƒ'(x) = 36x3 + 36x2 – 72x
ƒ'(x) = 36x(x2 + x – 2)
ƒ'(x) = 36x(x + 2)(x - 1)
While moving left to right on x-axis whenever derivative changes sign from negative to positive, we get local minima, and whenever derivative changes sign from positive to negative, we get local maxima.
