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What is the second derivative of $f(x)=3x^3+2x^2$?
1. $f''(x)=18x+4$
2. $f''(x)=9x^2+4x$
3. $f''(x)=18$
4. $f''(x)=0$
What are the critical numbers of the following equation?
$f(x)=3x^3+2x^2$
1. $x=-4/9, 0$
2. $x=4/9, 0$
3. $x=-9/4, 0$
4. $x=9/4, 0$
The sum to infinity of the geometric sequence $16, 8, 4, 2, ...$ is
1. $8$
2. $16$
3. $32$
4. $64$
What is the area under the curve for the function $f(x)=3x^3+2x^2$ on the closed interval $[-5,5]$?
1. $int_-5^5(3x^3+2x^2)dx=500/3$
2. $int_-5^5(3x^3+2x^2)dx=3/500$
3. $int_-5^5(3x^3+2x^2)dx=3$
4. $int_-5^5(3x^3+2x^2)dx=500$
On what intervals is the function $f(x)=3x^3+2x^2$ concave upwards and downwards?
1. concave upward $(-2/9, oo)$, concave downward $(-oo, -2/9)$
2. concave upward $(-oo, -2/9)$, concave downward $(-2/9, -oo)$
3. concave upward $(0, oo)$, concave downward $(-oo, 0)$
4. concave upward $(-oo, 0)$, concave downward $(0, oo)$
On what intervals is the function $f(x)=3x^3+2x^2$ increasing or decreasing?
1. increasing: $(-oo,-4/9) uu (0, oo)$, decreasing: $(-4/9, 0)$
2. increasing: $(-oo,-4/9)$, decreasing: $(-4/9, 0)$
3. increasing: $(-oo,0) uu (-4/9, oo)$, decreasing: $(-4/9, 0)$
4. increasing: $(-4/9, 0)$, decreasing: $(-oo,-4/9) uu (0, oo)$
What is the derivative of $f(x)=3x^3+2x^2$?
1. $f'(x)=9x^2+4x$
2. $f'(x)=3x^2+2x$
3. $f'(x)=0$
4. $f'(x)=12x^2+6x$
An equation of the line tangent to the graph of $y=cos(2x)$ at $x=pi/4$ is
1. $y-1=-(x-pi/4)$
2. $y-1=-2(x-pi/4)$
3. $y=2(x-pi/4)$
4. $y=-(x-pi/4)$
5. $y=-2(x-pi/4)$
What are all the values of $x$ for which the function $f$ defined by $f(x)=x^3+3x^2-9x+7$ is increasing?
1. $-3< x<1$
2. $-1< x< 1$
3. $x<-3$ and $x>1$
4. $x<-1$ and $x>3$