Common Core HSF.IF.B.4 worksheet

Question 1

Does the parabola y = −(x + 1)² − 3 have a maximum or a minimum point?

• A. Maximum
• B. Minimum

Question 2

Find d²y/dx² when y = −2x⁴ − 5x³ + 8x² − 7x + 3.

Answer 

Question 3

A drone's height (m) after t seconds is h = −t² + 12t − 29. What is its maximum height?

Answer 

Question 4

Use calculus to find the stationary point of y = −2x² − 16x − 29. Type it like (2, −1).

Answer 

Question 5

Find the vertex of y = x² − 6x + 3. Type it like (2, −1).

Answer 

Question 6

Where is f(x) = x³ + 3x² − 9x + 1 decreasing?

• A. −1 < x < 3
• B. x < −3 or x > 1
• C. x > 1
• D. −3 < x < 1

Question 7

For which values of x is f(x) = x² − 8x decreasing?

• A. x > −4
• B. x > 4
• C. x < −4
• D. x < 4

Question 8

B(h) is a phone's battery level (%) after h hours. B′(8) = −3. What does this mean?

• A. At that moment the battery is falling by about 3 percentage points per hour
• B. The average rate over the whole period
• C. The total change since the start
• D. The battery has 3% left

Question 9

Find the axis of symmetry of y = −x² + 10x − 26. Give the value of x.

Answer 

Question 10

f(x) = −3x³ − 3x² + 9x + 4. Find f″(−2).

Answer 

Question 11

Nia sketches −5x + 8y = 40 by joining its two intercepts. What is the area of the triangle formed by the line and the two axes?

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Question 12

Find the y-intercept of −x − 3y = 6. Type it like (4, 0).

Answer 

Question 13

What is the x-coordinate of the vertex of y = −x² + 8x − 23?

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Question 14

y = x³ − 9x² + 15x has a stationary point at x = 1. Is it a maximum or a minimum?

• A. Maximum
• B. Minimum

Question 15

The cost (in dollars) of making x phone cases is C(x) = 4x² + 52x + 200. Use C′(15) to estimate the extra cost of making one more case after 15.

Answer 

Question 16

What is the minimum value of f(x) = 3(x − 3)² + 3?

Answer