Derivative

When we "take the derivative" of a function what are we finding?

• What's a derivative?
• The rate at which our struggles in Calculus are increasing.
• The slope of the secant line
• The slope of the tangent line

Write the equation of the normal line of:  $f\left(x\right)=2x^2-\frac{1}{x}$  at x = 1

•  $y=-\frac{1}{5}x+\frac{4}{5}$  

•  $y=5x-6$  

•  $y-1=5\left(x-1\right)$  

•  $y-1=-\frac{1}{5}\left(x-1\right)$  

When you find the average rate of change over an interval, you are finding the slope of the _________________line on that interval.

When you are finding the instantaneous rate of change at a single point, you are finding the slope of the _____________ line at that point.

Find the average rate of change of Pete's height from 3 years old to 5 years old.

• 2 inches per year
• 8 inches per year
• 2 years
• 4 inches per year

The average rate of change on an interval is the...

• slope of the secant line on that interval

• slope of the tangent line on that interval

• slope of the cosecant line on that interval

• slope of the normal line on that interval

If the slope of the tangent line is 0, what does that mean with about the graph of the tangent line?

• Tangent line is vertical

• Tangent line has a positive slope

• Tangent line is horizontal

• Tangent line has a negative slope

Find the difference quotient for  $f\left(x\right)=x^2-2x-3$  .

• 2a - 2

• 2a - h - 2

• 2a + h - 2

• 2h - 2

If  $f\left(x\right)=x+5$  then find  $\frac{f\left(x+\Delta x\right)-f\left(x\right)}{\Delta x}$  

• 1

•  $x+\Delta x+5$  

•  $-x\ -\ 5$  

•  $\frac{\Delta x-5}{\Delta x}$  

If  $g\left(x\right)=x^2$  then what is  $\frac{g\left(x+\Delta x\right)-g\left(x\right)}{\Delta x}$  ?

•  $x^2+2x\Delta x+\Delta x^2$  

•  $2x^2+2x\Delta x+\Delta x^2$  

•  $2x+\Delta x$  

•  $2+\Delta x$