1997 AP Calculus BC Multiple Choice Question 5 Solution

In this video, we will solve the 1997 AP Calculus BC question number five from the multiple-choice section. The problem asks us to find the value of f'(2) given the function f(x) = (x - 1)^(3/2) + (e^(x - 2))/2. To differentiate the function, we use the power rule for the first term and the chain rule for the second term. After simplifying, we evaluate f'(2) and find that it equals 2. Therefore, the correct answer is choice C. If you found this helpful, please subscribe for more videos. Let's get started with the exercises

Exercise 1
Find the derivative of the function f(x) = x^3 - 2x^2 + 5x - 1.

Solution
To find the derivative, we differentiate each term separately
f'(x) = d/dx(x^3) - d/dx(2x^2) + d/dx(5x) - d/dx(1)
= 3x^2 - 4x + 5

Exercise 2
Find the derivative of the function g(x) = (2x + 1)^(1/2).

Solution
To find the derivative, we use the chain rule
g'(x) = (1/2)(2x + 1)^(-1/2) * d/dx(2x + 1)
= (1/2)(2x + 1)^(-1/2) * 2
= (1/2√(2x + 1)

Exercise 3
Find the derivative of the function h(x) = ln(x^2 + 3x).

Solution
To find the derivative, we use the chain rule and the power rule
h'(x) = 1/(x^2 + 3x) * d/dx(x^2 + 3x)
= 1/(x^2 + 3x) * (2x + 3)

These are the solutions to the exercises. If you have any questions, feel free to ask.
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