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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. $f''(x)=0$
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: $(-oo,-4/9) uu (0, oo)$
On $f(x)=2x^5+x^3-3x$
1. $(-0.65,1.4)$ is a relative and absolute maximum.
2. $(0.65,-1.4)$ is a relative and absolute minimum.
3. $(-0.65,1.4)$ is a relative maximum.
4. $(0.65,-1.4)$ is a relative minimum.
5. Both A and B.
6. Both C and D.
7. None of the above.
Differentiate. $f(x) = (4x^100)/25$
1. $f'(x) = (4x^99)/25$
2. $f'(x) = (8x^10) / 5$
3. $f'(x) = x^99 / 625$
4. $f'(x) = 16x^99$
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. $f'(x)=12x^2+6x$
Identify the intervals on which the given function is increasing and decreasing.
$f(x)=x^3+x^2-x$
1. Increasing: $(-oo, -1) uu (1/3,oo)$; decreasing: $(-1, 1/3)$
2. Increasing: $(-oo, -1)$; decreasing: $(-1, 1/3)$
3. Increasing for all x
4. Increasing: $(-1,1/3)$; decreasing: $(-oo, -1) uu (1/3,oo)$
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 $x>3$
5. All real numbers
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 $(0, oo)$
Find the intervals of increase and decrease for the following function. $f(x) = sqrt(3x^2 - 9x + 6)$
1. Increasing on $(3/2,oo)$ and decreasing on $(-oo, 3/2)$
2. Increasing on $(2,oo)$ and decreasing on $(-oo,1)$
3. Increasing on $(3/2,oo)$
4. Increasing on $(2,oo)$
Find the derivative. $f(x) = root[5](x^7)$
1. $f'(x) = root[5](7x^6)$
2. $f'(x) = 7/5 root[5](x^2)$
3. $f'(x) = root[4](x^6)$
4. $f'(x) = root[5](x^2)$
$f(x)=2x^5+x^3-3x$ is
1. increasing on $(-oo,oo)$.
2. decreasing on $(-oo,-0.65)cup(0.65,oo)$ and increasing on $(-0.65,0.65)$.
3. increasing on $(-oo,-0.65)cup(0.65,oo)$ and decreasing on $(-0.65,0.65)$.
4. decreasing on $(-oo,-1.4)cup(1.4,oo)$ and decreasing on $(1.4,-1.4)$.
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. $x=9/4, 0$
An equation of the line tangent to the graph of $y=cos(2x)$ at $x=pi/4$ is which of the following?
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. $y=-2(x-pi/4)$
Identify the intervals on which the given function is increasing and decreasing.
$f(x)=x^2 e^(-x^2)$
1. Increasing: $(-oo, -1) uu (0,1)$; decreasing: $(-1, 0) uu (1,oo)$
2. Increasing: $(-oo, 0)$; decreasing: $(0, oo)$
3. Increasing for all x
4. Increasing: $(-1,0) uu (1,oo)$; decreasing: $(-oo, -1) uu (0,1)$
$f(x)=x^3+x^2-x$
1. Relative maximum: $(-1, 3/2); \$ relative minimum: $(1/3, -1)$
2. Relative maximum: $(-1, 1); \$ absolute minimum: $(1/3, -5/27)$
3. Relative maximum: $(-1, 1); \$ relative minimum: $(1/3, -5/27)$
4. Relative maximum: $(-1, 3/2); \$ no relative or absolute minimums