Week8a

Clicker Questions

Question 1.

Let $f(x)=\sqrt{x}+\dfrac{3}{x}$. Find $f'(x)$.

a) $\dfrac{1}{\sqrt{x}}+3$

b) $\dfrac{2}{\sqrt{x}}-3x^{-2}$

c) $\dfrac{1}{2\sqrt{x}}+\dfrac{3}{x^2}$

d) $\dfrac{1}{2\sqrt{x}}-\dfrac{3}{x^2}$

Question 2.

Find the slope of the tangent line to the curve $y=\pi+2x^{3/2}$ at $x=9$.

a) $\pi + 9$

b) $\pi + 3x^{1/2}$

c) $3x^{1/2}$

d) $9$

Question 3.

Let $f(x)=(2x+1)^2$. Find $f'(x)$.

a) $2(2x+1)$

b) $8x$

c) $8x+1$

d) $8x+4$

Question 4.

Find the equation of the tangent line to the curve $y=x^2(x^2-1)$ at $x=2$.

a) $y=28x+2$

b) $y=28x-44$

c) $y=28x+12$

d) $y=8x-4$

Question 5.

Which of the following describes the derivative function $f'(x)$ of a quadratic function $f(x)$?

a) Constant

b) Linear function

c) Quadratic function

d) Cubic function

Question 6.

Which of the following does NOT equal $\dfrac{d}{dx}(4x^3-6x^{-2})$?

a) $12x^2+\dfrac{12}{x^3}$

b) $\dfrac{12x^5+12}{x^3}$

c) $\dfrac{12x^2+12}{x^3}$

d) $12(x^2+x^{-3})$

Question 7.

Find ALL points on the graph of $f(x)=x^4-2x^2$ where the tangent line is horizontal.

a) $x=0, 1$

b) $x=1, -1$

c) $x=0, 1, -1$

d) $x=0, \sqrt{2}, -\sqrt{2}$

Question 8.

Let $g(5)=1$, $h(5)=2$, $g'(5)=3$ and $h'(5)=-1$, find $f'(5)$ for $f(x)=2g(x)+xh(x)$.

a) $x=-1$

b) $x=1$

c) $x=3$

d) $x=5$

Question 9.

If $x^2+y-8=0$, find $\dfrac{dy}{dx}$.

a) $0$

b) $2x$

c) $-2x$

d) Cannot be determined.

Question 10.

Let $f(x)=3^x$. Find $f'(x)$.

a) $x3^{x-1}$

b) $3^x$

c) $0$

d) Cannot be determined from what we know.

Question 11.

Let $f(x)=\dfrac{x^2+7}{x}$. Find $f'(x)$.

a) $2x+7$

b) $x+7$

c) $1$

d) Cannot be determined from what we know.

Question 12.

Let $f(x)=\dfrac{x}{x^2+7}$. Find $f'(x)$.

a) $\dfrac{1}{2x+7}$

b) $-\dfrac{1}{x^2}$

c) $1$

d) Cannot be determined from what we know.

Question 13.

Let $f(x)=\dfrac{x}{x^2+7}$. Find $f'(x)$.

a) $\dfrac{1}{2x+7}$

b) $-\dfrac{1}{x^2}$

c) $1$

d) Cannot be determined from what we know.

Question.

Let $f(3)=2$, $f'(3)4$, $g(3)=1$ and $g'(3)=3$, find $h'(3)$ for $h(x)=\dfrac{f(x)}{g(x)}$.

a) $-2$

b) $2$

c) $-2/9$

d) $2/9$

Question 14.

Let $f(x)=x^2+y^2+xy$. Find $f'(x)$.

a) $2x+2y+1$

b) $2x+y$

c) $2x$

d) Cannot be determined from what we know.