Basic Differentiation Rules

Given  $f\left(x\right)=3x^2+2x-1$  , which of the following is the correct derivative?

•  $f'\left(x\right)=6x^2+2$  

•  $f'\left(x\right)=6x+2$  

•  $f'\left(x\right)=6x^2+2$  

•  $f'\left(x\right)=6x^2+2x^2-x$  

The derivative of a function at a given point,  $c$  , ie equal to which of the following

• The slope of the secant line through c

• The slope of the vertical line through c

• The slope of the horizontal line through c

• The slope of the line tangent to the function at c

Which of the following is the correct definition of the Power Rule of derivatives?

• Given $f\left(x\right)=x^n$ , $f'\left(x\right)=x^{n-1}$

• Given $f\left(x\right)=x^n$ , $f'\left(x\right)=nx^{n-1}$

• Given $f\left(x\right)=x^n$ , $f'\left(x\right)=\frac{x^{n-1}}{n}$

• Given $f\left(x\right)=x^n$ , $f'\left(x\right)=\frac{n}{x^{n-1}}$

Who is more beautiful?

• Jennifer Aniston

• Angelina Jolie

Given $f\left(x\right)=17$  , what is the derivative of  $f\left(x\right)$  ?

•  $f'\left(x\right)=17x$  

•  $f'\left(x\right)=17$  

•  $f'\left(x\right)=0$  

•  $f'\left(x\right)=17x^2$  

Given the piecewise function above, describe the continuity and differentiability of f(x) when x = 2.

• Continuous but not differentiable

• Differentiable but not continuous

• Neither continuous nor differentiable

• Both continuous and differentiable

Given $f\left(x\right)=\frac{2x^2+4x-6}{4x}$  , find  $f'\left(x\right)$  .

•  $f'\left(x\right)=\frac{4x+4}{4}$  

•  $f'\left(x\right)=x+1$  

•  $f'\left(x\right)=\frac{x^2+2x-3}{2x}$  

•  $f'\left(x\right)=\frac{1}{2}+\frac{3}{2x^2}$  

Given $f\left(x\right)=3x$  , which of the following is the derivative of the function?

•  $h'\left(x\right)=3$  

•  $q'\left(x\right)=3$  

•  $b'\left(x\right)=3$  

•  $f'\left(x\right)=3$  

What is the derivative of 0?

• You can't take the derivative of 0.

• 0

• This is all derivative.

• Any constant

Select all of the following choices that are ingredients in a Big Mac.

• cheese

• pickles

• mustard

• tomato

• ketchup