53
MCQ (Single Correct Answer)
The smallest value of polynomial $x^3-18 x^2+96 x$ in $[0,9]$ is
A
126
B
0
C
135
D
160
54
MCQ (Single Correct Answer)
The function $f(x)=2 x^3-3 x^2-12 x+4$, has
A
two points of local maximum
B
two points of local minimum
C
one maxima and one minima
D
no maxima or minima
55
MCQ (Single Correct Answer)
The maximum value of $\sin x \cdot \cos x$ is
A
$\frac{1}{4}$
B
$\frac{1}{2}$
C
$\sqrt{2}$
D
$2 \sqrt{2}$
56
MCQ (Single Correct Answer)
At $x=\frac{5 \pi}{6}, f(x)=2 \sin 3 x+3 \cos 3 x$ is
A
maximum
B
minimum
C
zero
D
neither maximum nor minimum
57
MCQ (Single Correct Answer)
The maximum slope of curve $y=-x^3+3 x^2+9 x-27$ is
A
0
B
12
C
16
D
32