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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 $f(x)=2x^5+x^3-3x$
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.
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. $f'(x)=12x^2+6x$
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. $x=9/4, 0$
What is the limit of $f(x)=3x^3+2x^2$ as $x$ approaches 5?
1. $lim_(x->5)f(x)=425$
2. $lim_(x->5)f(x)=452$
3. $lim_(x->5)f(x)=542$
4. $lim_(x->5)f(x)=245$