By how much is the mean of 30, 56, 31, 55, 43 and 44 less than the median?
0.75
0.50
0.33
0.17
Correct answer is C
\(Mean = \frac{30+56+31+55+43+44}{6}\\=\frac{259}{6}=43.167\\Median = 30,31,43,44,55,56\\=\frac{43+44}{2}=\frac{87}{2}=43.5\\Median-mean = 43.5-43.17=0.33\)
Determine the maximum value of y = 3x2 - x3
zero
2
4
6
Correct answer is C
y = 3x2 - x3
dy/dx = 6x - 3x2
as dy/dx = 0
6x - 3x2 = 0
3x (2 - x) = 0
this implies that 2 -x = 0 and 3x = 0
x = 2 (or) 0
But = dy/dx = 6x - 3x2
d2y/dx2 = 6 - 6x at x = 2
= 6 - 6(2)
= -6
y = 3x2 - x3
= 3(2)2 - 23
= 12 - 8
= 4
12x cos (4x)
-12x cos (-4x)
-12 cos (-4x)
12 sin (-4x)
Correct answer is C
y = 3 sin(-4x)
dy/dx = 3 x - 4 cos (-4x)
= -12 cos (-4x)
Evaluate \(\int^{2} _{3}(x^2 - 2x)dx\)
4
2
4/3
1/3
Correct answer is C
\(\int^{2} _{3}(x^2 - 2x)dx\\=\left[\frac{x^3}{3}-\frac{2x^2}{2}\right ]^{2}_{3}\\\left[\frac{x^3}{3}-x^2 + C\right ]^{2}_{3}\\\left[\frac{3^3}{3}-3^2 + C \right ]-\left[\frac{2^3}{3}-2^2 + C \right ]\\9-9-\left[\frac{8}{3}-4 \right ]\\=\frac{-8}{3}+4\\=\frac{4}{3}\)
Find the slope of the curve y = 2x\(^2\) + 5x - 3 at (1, 4).
4
6
7
9
Correct answer is D
y = 2x\(^2\) + 5x - 3
dy/dx = 4x + 5
= 4 + 5
= 9