Derivatives #1

Find the derivative,  $f'\left(x\right)$  , of
 $f\left(x\right)=-\frac{2}{3}x^3-\frac{1}{2}x^2+9x$  

•  $-2x^2-x+9$  
  

•  $-2x^3-x^2+9x$  
  

•  $-\frac{2}{12}x^4-\frac{1}{6}x^3+\frac{9}{\ 2}x^2$  
  

•  $-2x^4-x^3+9x^2$  
  

Which of the following is the derivative,  $f'\left(x\right)$  , of  $f\left(x\right)=\left(3x^4-7\right)\left(5x^2+1\right)$  

•  $\left(12x^3\right)\left(10x\right)$  
  

•  $\left(3x^4-7\right)\left(10x\right)+\left(12x^3\right)\left(5x^2+1\right)$  
  

•  $\left(3x^4-7\right)\left(10x\right)-\left(12x^3\right)\left(5x^2+1\right)$  
  

•  $\frac{3x^4-7}{10x}+\frac{12x^3}{5x^2+1}$  
  

Which of the following is the derivative, f′(x), of:

f(x) = x² - cosx

• f"(x) = 2 + cosx

• f"(x) = 2x + cosx

• f"(x) = 2x - cosx

• f"(x) = 2x + sinx

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.HSF.IF.A.2

Which of the following is the derivative,  f′(x), of:   $f\left(x\right)=\frac{1}{3x^2}+4x^3$  

•  $6x^3+12x^2$  

•  $6x^{ }+12x^2$  
  

•   $\frac{-2}{3x^3}+12x^2$  

•  $\frac{6}{x^2}+12x^2$  
  

Which function has the derivative of g'(x) = 4x³ + 2x - 1

• g(x) = 2x⁴ + 2x² - 1

• g(x) = x⁴ + x² - x

• g(x) = 2x³ + x³ - 2x

• g(x) = x⁵ + x² - x

Tags

CCSS.HSA.APR.A.1

At which point(s) will the slopes of the tangent line are zero?

• at C only

• at points A, C and E only

• at point B and D only

• at points A and E only

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

Let f(x) = (x - 1)(x + 2).

Find f'(0).

• 0

• 1

• 2

• 3

Tags

CCSS.HSF.IF.A.2

At what point will the slope of y = -x² + 4 is zero?

• (0, 4)

• (1, 4)

• (4, 0)

• (1, 0)

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

CCSS.HSA.REI.D.10

What is the equation of the line tangent to the curve y = x² at x = 1?

• y = 2x + 1

• y = 2x - 1

• y = -2x + 1

• y = x - 1

Tags

CCSS.HSA.REI.C.7

CCSS.HSG.GPE.B.5