Application of differentiation

If x = 200 is the critical number of a function g and  $g''\left(200\right)>0$  then, g has a local maximum at x = 200.

• True

• False

Extremum points are either

• local maximum

• fixed point

• inflection point

• local minimum

Differentiate with respect to x...

• 16x + 4x^-2

• 16x - 4x^-2

• 16x + 4x

• 16x - 4x

Stationary point occur when....

• x = 0

• $\frac{\text{d}y}{\text{d}x}=0$
  

• $\frac{\text{d}x}{\text{d}y}=0$

• $\frac{d^2y}{dx^2}=0$

Differentiate with respect to x...

• 6x² + 4x

• 9x + 4

• 9x² + 4x

• 6x² + 4

 $\lim_{x\rightarrow-5}\ \ \ \frac{x+5}{2}\ =\ ....$  

• 0

• 5

•  $\infty$  

•  $\frac{5}{2}$  

•  $\frac{2}{5}$  

What is the stationary points for the curve f(x) = x³ +3x² - 24x and determine their nature.

• Maximum point : (2, -28) and minimum point : (-4, 80)

• Minimum point : (2, 28) and maximum point : (-4, 80)

• Minimum point : (2, -28) and maximum point : (4, 80)

• Minimum point : (2, -28) and maximum point : (-4, 80)

Over what interval(s) is f(x) increasing?

• (-∞, -3) ∪ (1, ∞)
• (-3, 1)
• (-5, 0) ∪ (2, ∞)
• (-5, ∞)

Find the derivative of f(x) = 2x²+3.

• 4x
• 4x²
• 3
• 4x+3

 $\lim_{x\rightarrow\infty}\ \frac{2x+6}{x-6}=...$  

• 1

• 2

• 3

• 4

•  $\infty$