Derivatives and Integration

What is differentiation?

• The process of finding the derivative of a function.

• The process of finding the integral of a function.

• The process of finding the difference of a function.

• The process of finding the sum of a function.

The derivative of f(x) = 5 is ________.

• 1

• 5c

• 5x

• 0

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

Find the slope of the tangent line to the graph of the function at the given point.

f(x) = 5 - x² (3,-4)

• m = -6

• m = 6

• m = 5

• m = 3

^{∫ 2x+4 dx}

• x² + 4x + c

• 2

• x² + 4x

• 2x² + 4x + c

∫(4 - 18x) dx

• F(x) = -18

• F(x) = 4x - 9x²

• F(x) = 4x - 9x² + C

• F(x) = (4 - 18x)² /2 + C

∫ - sinx dx

• -cos x + C

• cos x + C

• tan x + C

• 1/√1- x²

How many derivatives can you take of a function?

• only 3
• only 2
• only 1
• until you can no longer derive it

Find the second derivative of the function:
f (x) =  2x - 5x⁶

• f ''(x)= 2 - 30x
• f ''(x) =  2-30x⁵
• f ''(x) = -30x⁵
• f ''(x) = -150x⁴

Tags

CCSS.HSA.APR.A.1

Find f "'(x) when

f(x)=10x⁵ +3x⁴ -5x³ +2x² -10x+6

• 200x³+36x² -30x+4

• 600x² +72x -26

• 600x² +72x -30

• 600x² +72x -36

Find the derivative of y = 2x² (3x - 4)

• 6x³ - 8x²
• 18x² - 16x
• 15x² - 6x
• 6x - 4