Differentiation

What is the derivative of

 $\sqrt{x^3}$  

•  $\frac{3\sqrt{x}}{2}$  

•  $\frac{1}{2\sqrt{x}}$  

•  $\frac{3}{2\sqrt{x}}$  

•  $\frac{\sqrt{x}}{2}$  

What is the derivative of  $\frac{1}{\sqrt{x}}$  

•  $\frac{\sqrt{x^3}}{2}$  

•  $\frac{-\sqrt{x^3}}{2}$  

•  $\frac{-\sqrt{x}}{2}$  

•  $\frac{\sqrt{x}}{2}$  

Find the x-coordinates of the points on the graph of $f\left(x\right)=\frac{2}{3}x^3-\frac{9}{2}x^2-3x+8$  when the gradient is 2

•  $x=0.5\ and\ 5$  

•  $x=-0.5\ and\ 5$  

•  $x=0.5\ and\ \ -5$  

•  $x=-0.5\ and\ -5$  

Find the equation of the normal to $y=\frac{1-2x}{x^2}$ at the point (2,-0.75) 

•  $y=-4x+\frac{35}{4}$  

•  $y=4x+\frac{29}{4}$  

•  $y=-4x-\frac{35}{4}$  

•  $y=-4x+\frac{29}{4}$  

Find the equation of the tangent to the curve $6\left(1-2x\right)^{\frac{1}{3}}$ at x = 0 

•  $y=-4x+6$  

•  $y=4x+6$  

•  $y=-4x-6$  

•  $y=4x-6$  

Find the minimum length of fencing required and the value of x for which this minimum occurs

• $3\sqrt{2}and\ 12\sqrt{2}$

• $5\sqrt{2}and\ 20\sqrt{2}$
  

• $4\sqrt{2}and\ 20\sqrt{2}$

• $\sqrt{32}\ and\ \ 10\sqrt{2}$

Answer the following question

• 18, $10000

• 19, $9000

• 20, $10000

• 19.5, $9999

Answer the following question

• $100

• $150

• $164

• $158

• 5 s and 11 m

• 5.5 s and 11.25 m

• 5.4 s and 11.1 m

• 5.5 s and 11 m

Find the local maximum and minimum (extrema) on the given function

• $\left(0,2\right),\left(\frac{\pi}{2},-1\right)$

• $\left(0,2\right)$
  

• $\left(0,2\right),\left(\frac{\pi}{2},-1\right),\left(\pi,2\right)$

• $\left(\frac{\pi}{2},-1\right)$