Application of Derivatives

If the angle of intersection of two curves is a right angle, then two curves are called (a)  

A fn is said to be decreasing if f'(x) is

• $\ge0$

• $\le0$

• $=0$

• $\ne0$

What is the decreasing interval(s) on the function shown?

• $\left(-7,\ -6\right)\ and\ \left(-2,\ 4\right)$

• $\left(-7,\ 0\right)\ and\ \left(-2,\ 4\right)$

• $\left(-7,\ -6\right)\ and\ \left(-2,\ 0\right)$

• $\left(-7,\ 0\right)\ and\ \left(4,\ 5\right)$

Maximum value of the function $f\left(x\right)=\left(x-2\right)^2+1$ is 

• 1

• 3

• 2

• none of these

Determine the point on the curve f(x)=(2x-1)² where the tangent is parallel to the line y=4x-2

• (0 , 1)

• (1 , 9)

• (1/2 , 0)

• (1 , 1)

The minimum value of  $\frac{x}{\log_ex}$  is

• (A)  e

• (B)  1/e

• (C)  1

• (D)  None of these

The absolute minimum value of x⁴ – x² – 2x+ 5

• is equal to 5

• is equal to 3

• is equal to 7

• does not exist

Use differential to approximate  $\sqrt{36.6}$  

• 6.01

• 6.05

• 6.1

• 6.09

The curve y = x^1/5 has at (0, 0)

• (a) a vertical tangent (parallel to y-axis)

• (b) a horizontal tangent (parallel to x-axis)

• (c) an oblique tangent

• d) no tangent

 $The\ function\ f\left(x\right)=\ x^2-8x+12\ is\ strictly\ decrea\sin g\ in$  

•  $\left(-\infty,\ \infty\right)$  

•  $\left(2,\ 6\right)$  

•  $\left(-\infty,\ 4\right)$ 

•  $\left(4,\ \infty\right)$