Understanding Slope and Function Values

The video tutorial explores how to determine the largest possible value of f(10) for a differentiable function f, given that f(-2) = 3 and the derivative f'(x) is less than or equal to 7 for all x. The instructor encourages viewers to attempt solving the problem independently before guiding them through the solution. The process involves visualizing the function on a graph, understanding the constraints on the slope, and calculating the maximum value of f(10) by assuming the slope remains at its maximum possible value of 7. The final calculation shows that f(10) can reach a maximum value of 87.

What is the value of f(-2) given in the problem?

• 4

• 1

• 2

• 3

What is the maximum value of f'(x) for all x?

• 7

• 6

• 5

• 8

What is the first step suggested to solve the problem?

• Ask a friend

• Pause the video and think

• Use a calculator

• Skip the problem

What is the significance of the slope in finding f(10)?

• It is irrelevant

• It helps in finding the maximum value

• It changes the function type

• It determines the color of the graph

What is the assumed slope to find the maximum value of f(10)?

• 7

• 8

• 5

• 6

What is the change in x from -2 to 10?

• 10

• 11

• 12

• 13

What is the change in y if the slope is 7 and change in x is 12?

• 108

• 72

• 96

• 84

What is the final calculated value of f(10)?

• 88

• 87

• 86

• 85

If the slope is less than 7, what happens to the value of f(10)?

• It becomes undefined

• It increases

• It decreases

• It remains the same

What is the increase in f(x) from f(-2) to f(10) with a slope of 7?

• 83

• 82

• 84

• 81