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# Derivatives Questions - All Grades

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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 $(0, oo)$
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. $f''(x)=0$
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: $(-oo, -1) uu (1/3,oo)$
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. $f'(x) = root[5](x^2)$
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. $f'(x)=12x^2+6x$
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. $f'(x) = 16x^99$
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.
Find the derivative. $f(x) = 2x^0.4 - 8x^(-0.02)$
1. $f'(x) = 2x^(-0.4) - 8x^(-1.02)$
2. $f'(x) = 0.8x^(-0.6) + 0.16x^(-1.02)$
3. $f'(x) = 2 + 0.16x^(-1.02)$
4. $f'(x) = 0.5x^(-0.6) + 0.4 x^(-1.02)$
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 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
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 $(2,oo)$
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: $(-oo, -1) uu (0,1)$
Identify and classify the extrema of the given function.
$f(x)=x^3+x^2-x$
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
Differentiate. $f(x) = 3x^-2 + 5x^-3 - 2x^-5$
1. $f'(x) = -6x^-1 - 15x^-2 + 10x^-4$
2. $f'(x) = 3x^-3 + 5x^-4 - 2x^-6$
3. $f'(x) = 3x^-1 + 5x^-2 - 2x^-4$
4. $f'(x) = -6x^-3 - 15x^-4 + 10x^-6$
Find $d/dx(tan^-1((x-sqrt(a^2-x^2))/(x+sqrt(a^2-x^2))))$.
1. $-1/(sqrt(a^2-x^2$
2. $1/(sqrt(a^2-x^2$
3. $sqrt(a^2-x^2$
4. $x/(sqrt(a^2-x^2$
$f(x)=3x^3+2x^2$
1. $x=-4/9, 0$
2. $x=4/9, 0$
3. $x=-9/4, 0$
4. $x=9/4, 0$