Calculus Derivatives & Difference Quotient

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

• 1

•  $x+\Delta x+5$  

•  $-x\ -\ 5$  

•  $\frac{\Delta x-5}{\Delta x}$  

Tags

CCSS.8.EE.B.5

If  $h\left(x\right)=x^2-3$  then what is  $\frac{h\left(x+\Delta x\right)-h\left(x\right)}{\Delta x}$  

•  $x^2+2x\ \Delta x+\Delta x^2$  

•  $x^2+2x\ \Delta x+\Delta x^2-3-x^2+3$  

•  $\frac{2x^2+2x\Delta x+x^2-6}{\Delta x}$  

•  $2x+\Delta x$  

Tags

CCSS.HSF.IF.B.6

• 4

• 5

• 6

• 7

Find the derivative of $f\left(x\right)=-2x^2+4x+6$ .

•  $-4x$  

•  $-4x+\text{4}$  

•  $-2x+4$  

•  $-4x+10$  

Differentiate y= x³ + 2x

• 3x³+2x
• 3x²+2
• 3x+2
• 3x

Find the difference quotient when f(x) = x² - x + 1

• 2x - 1 + h
• 4x - 5 - h
• -2x - 1 + h 
• x² + 2h

Tags

CCSS.HSF-BF.A.1C

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

• 7
• 0
• 7x
• 14

Find the derivative of  $f\left(x\right)\ =\ \frac{1}{x^5}$  

•  $5x^4$  

•  $-5x^6$  

•  $-\frac{5}{x^6}$  

•  $\frac{1}{5x^6}$  

Find the derivative of f(x) = 6x³⁰ -2x¹⁵ + 4x³ - 2x + 1

• f'(x) = 18x²⁹ + 30x¹⁵ + 12x³ 
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² 
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² - 2
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² +1

Tags

CCSS.HSA.APR.A.1

FInd the derivative:
f(x) = (-2/3)x³ - (1/2)x² + 9x

• -2x² - x + 9
• -2x² + x + 9
• 2x² - x + 9
• 2x² - x - 9

Tags

CCSS.HSA.APR.A.1