application of derivative

y=6x-3. Find increasing and decreasing intervals?

• decreasing on $\left(-\infty;+\infty\right)$

• increasing on $\left(-\infty;+\infty\right)$

• increasing on $\left(-\infty;6\right)\cup\left(6;+\infty\right)$

• decreasing on $\left(-\infty;6\right)\cup\left(6;+\infty\right)$

 $f\left(x\right)=x^{\frac{3}{4}}-4$  Find the critical points?

• no critical points

• x=0

•  $x\ge0$  

• 1

 $f\left(x\right)=2x^3+7x^2-12x+4$  Find the local extrema.

•  $x_{\max}=-3,\ x_{\min}=\frac{2}{3}$  

•  $x_{\min}=-3,\ x_{\max}=\frac{2}{3}$  

•  $x_{\max}=3,\ x_{\min}=-\frac{2}{3}$  

• no local extremas

 $f\left(x\right)=\frac{x^3}{3}-\frac{5x^2}{2}+6x-3,\ \left[1,4\right]$  Find the absolute extrema of each function on the given interval.

•  $y_{\min}=\frac{5}{6},\ y_{\max}=\frac{7}{3}$  

•  $y_{\max}=\frac{5}{6},\ y_{\min}=\frac{7}{3}$  

•  $y_{\min}=\frac{6}{5},\ y_{\max}=\frac{3}{7}$  

•  $y_{\max}=\frac{6}{5},\ y_{\min}=\frac{3}{7}$  

 $f\left(x\right)=x^3-ax^2-bx+4$  Given the function which has an inflection point at (1, -2). Find a,b?

• a=3, b=4

• a=4, b=3

• a=0, b=3

• a=4,b=3

A man has 60m of fencing that he plans to use to enclose a rectangular garden plot. Find the dimensions of the plot that will maximize the area.

• 15m, 15m

• 30m, 30m

• 10m,10m

• no answer

 $f\left(x\right)=\frac{mx^2+1}{x-1}$  

For what values of m does the given function has no local extrema? 

• -1,0

• 1,0

• 0

• -2,0