Basic Derivatives Quiz

When you plug a given point into the derivative of a function, you get this.

• tangent line

• normal line

• slope

• average rate of change

This is a line that touches the function at a given point and has a slope that is equal to the instantaneous rate of change at a given point.

• normal line

• tangent line

• delta line

• secant line

Using the limit definition of the derivative, find the derivative of  $f\left(x\right)=\sqrt{x-7}$  

•  $0$  

•  $f'\left(x\right)=\frac{1}{2\sqrt{x-7}}$  

•  $\frac{1}{\sqrt{x-7}}$  

•  $\frac{1}{2}\sqrt{x-7}$  

What is  $\lim_{h\rightarrow0}\frac{\left[\left(x+h\right)^3-x^3\right]}{h}$  

•  $-x^3$  

•  $-3x^2$  

•  $3x^2$  

• The limit does not exist

Find the derivative of the given function
f(x) = 7

• 7
• 0
• 7x
• 14

What is the derivative of xⁿ?

• (n-1)xⁿ
• nxⁿ⁺¹
• (n+1)x^n-1
• nx^n-1

f(x)= 5/x^{2
f'(x) =} 

• 5x
• 5/2x
• 5x^-2
• -10/x³

 $f'\left(\frac{1}{2}\right)$  Use the graph to find

• -3

•  $\frac{3}{2}$  

•  $\frac{1}{2}$  

•  $-\frac{7}{2}$  

For what values of x will f'(x)=0?

• -3, -1, 0, 3

• -3, -1, 0

• -1, 0

• -3

For what values of x is f(x) NOT differentiable?

• -2, -1, 0, 2, 3

• -3, -2, -1, 0, 2, 3

• -2, -1, 0, 2

• 2, 3