curve sketching calculus

The graph shown is the DERIVATIVE of f. From the derivative's graph, identify the interval graph where f (the original function) is concave up.

• (-1,1) & (3,4)
• (-3,-2)
• (-2,-1)
• (-3,-1) & (1,3)

If a function's FIRST derivative is negative at a certain point, what does that tell you?

• The function is increasing at that point
• The function is decreasing at that point
• The concavity of the function is up at that point
• The concavity of the function is down at that point

What are the intervals of the graph increasing for f(x) = 2x⁴- 4x² + 1

• (-1,0)

• (0,1)

• (-∞,-1) and (0,1)

• (1,∞) and (-1,0)

What is the maximum value of f(x) = x³ - 3x² - 1 on the interval [-3, 2]?

• 0
• -1
• 2
• 5

When you find the average rate of change over an interval, you are finding the slope of the _________________line on that interval.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Find the average rate of change of Pete's height from 3 years old to 5 years old.

• 2 inches per year
• 8 inches per year
• 2 years
• 4 inches per year

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

The average rate of change on an interval is the...

• slope of the secant line on that interval

• slope of the tangent line on that interval

• slope of the cosecant line on that interval

• slope of the normal line on that interval

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

If the slope of the tangent line is 0, what does that mean with about the graph of the tangent line?

• Tangent line is vertical

• Tangent line has a positive slope

• Tangent line is horizontal

• Tangent line has a negative slope

State the slope of the line given.

• Positive

• Negative

• Zero Slope

• Undefined

Tags

CCSS.8.EE.B.5

What is the slope of the line normal to the curve y = x² + x at x = 1?

• -1

• -1/2

• -1/3

• -1/4