JEE Main 30 June 2022 Shift 1 Solved Paper

Given,
f(x)=4x3−11x2+8x−5
∴f′(x)=12x2−22x+8
=2(6x2−11x+4)
=2(6x2−8x−3x+4)
=2[2x(3x−4)−1(3x−4)]
=2[(3x−4)(2x−1)]f′(x) is positive before ‌

1

2

means slope of f(x) is positive before ‌

1

2

and f′(x) is negative after ‌

1

2

means slope of f(x) is negative after ‌

1

2

.∴ At ‌

1

2

,f(x) is local maximum
Also, f′(x) is negative before ‌

4

3

means slope of f(x) is negative before ‌

4

3

and f′(x) is positive after ‌

4

3

means slope of f(x) is positive after ‌

4

3

.∴ At ‌

4

3

,f(x) is local minimum
From wavy curve method,
f′(x)>0,∀x∈(−α,‌

1

2

)∪(‌

4

3

,α)
∴f(x)‌ increasing in ‌x∈(−α,‌

1

2

)∪(‌

4

3

,α)
f′(x)<0‌∀x∈(‌

1

2

,‌

4

3

)
∴f(x)‌ decreasing in ‌x∈(‌

1

2

,‌

4

3

)