Finding Constants and Integrating Functions

The video tutorial explains how to find the value of f(4) given f'(x) = 9x^2 + 10x and f(1) = 7. It involves integrating the derivative to find f(x) + C, applying the power rule of integration, simplifying the expression, solving for the constant C using the given f(1) = 7, and finally calculating f(4) by substituting the values into the derived function.

What is the given derivative function f'(x)?

• 9x^2 + 10x

• 9x^3 + 10x^2

• 3x^3 + 5x^2

• x^2 + 10x

What is the first step in finding f(x) from f'(x)?

• Solve for x

• Integrate f'(x)

• Differentiate f'(x)

• Substitute x = 1

Which rule is applied to integrate f'(x)?

• Chain Rule

• Power Rule

• Quotient Rule

• Product Rule

What is the integral of 9x^2 with respect to x?

• 9x^3/3

• 3x^3

• x^3/3

• 9x^3

What is the simplified form of the integrated function f(x)?

• 3x^3 + 5x + C

• 9x^2 + 10x + C

• x^3 + x^2 + C

• 3x^3 + 5x^2 + C

How do we find the constant C?

• By integrating f(x)

• By differentiating f(x)

• By using the condition f(1) = 7

• By solving f'(x) = 0

What is the value of C when f(1) = 7?

• 7

• -1

• 1

• 0

What is the expression for f(x) after finding C?

• 3x^3 + 5x^2 - 1

• 3x^3 + 5x^2 + 1

• 3x^3 + 5x^2

• 9x^2 + 10x - 1

What is the value of f(4)?

• 80

• 64

• 271

• 192

Which of the following steps is necessary to calculate f(4)?

• Substitute x = 4 into f(x)

• Solve f'(x) = 0

• Differentiate f(x)

• Integrate f(x)