Intro to Calculus 4.1

Given that f(x) = x² - 3x, which of the following represents f(x + h)

• x² - 3x + h
• x + h² - 3x + h
• (x + h)² - 3(x + h)
• x² + h - 3x + h

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

TRUE or FALSE: f ' (-1) = 3 means the slope of the the function f(x) at x = -1 is 3. 

• TRUE
• FALSE

• The slope of f(x) when x = 2 is 3.
• The slope of f(x) when x = 3 is 2. 
• The slope of f(x) at any value of x is 2.
• The slope of f(x) at any value of x is 3.

• The slope of f(x) at any value of x is 3.
• The slope of f(x) at x = 0 is 2.
• The slope of f(x) at any value of x is given by 3x-1. 
• The slope of f(x) at x=0 is given by 3x-1. 

If f(2)=3 and f'(2)=-1, then the equation of the tangent line to f(x) at x = 2 is 

• y - 2 = 3(x + 1)
• y - 3 = -1(x - 2)
• y + 1 = 2(x - 3)
• y - 1 = 2(x - 3)

Tags

CCSS.HSA.CED.A.2

CCSS.HSF.BF.A.1

CCSS.HSF.IF.A.2

CCSS.HSF.IF.C.7

CCSS.HSF.LE.A.2

The derivative of a function tells you about

• Instantaneous slope of the function
• The value of the function
• The rate at which x is changing
• The average value of the function

Derivative means the same thing as

• slope of the tangent line

• slope of the normal line

• the degree of the function

• the rate at which y is changing

Find the slope of      y= 3x² - 5 using the point x=2

• 10
• 11
• 12
• 13

Tags

CCSS.8.EE.B.5

Find the value of the derivative at the indicated x-value.

• -12
• 5
• 10
• -13

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

Find an equation of the tangent line to the graph of the function at the point f(x) = x^2 + 3x + 6 at the point (–3,6).

• y = -9x - 21

• y = -3x - 3

• y = 3x

• y = -3

• y = 9x