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Describe the end behavior of $f(x)=2^x-3$.
1. $"As " x -> -oo, y-> -3; \ "as " x->oo, y->oo$
2. $"As " x -> -oo, y-> oo; \ "as " x->oo, y->oo$
3. $"As " x -> -3 , y-> oo; \ "as " x->oo, y->oo$
4. $"As " x -> -oo, y-> oo; \ "as " x->oo, y->-3$
Find the average rate of change of $f(x)=-4x^2+3x-4$ on the interval $[-1, 3]$.
1. $-1/5$
2. $5$
3. $1/5$
4. $-5$
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.
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. $x=9/4, 0$
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 $(0, oo)$
The sum to infinity of the geometric sequence $16, 8, 4, 2, ...$ is
1. $8$
2. $16$
3. $32$
4. $64$
What is $d/dx(x^lnx)$?
1. $x^lnx$
2. $(lnx)^x$
3. $(2/x)(lnx)(x^lnx)$
4. $(lnx)(x^(lnx-1))$
5. $2(lnx)(x^lnx)$
$f(x)=2x^5+x^3-3x$ 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 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. $int_-5^5(3x^3+2x^2)dx=500$
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 $x>3$