Find the value of c which satisfies the Mean Value Theorem for given function, f(x) = x^2 + 2x + 1 on [1,2]?
- 13/2
- 7/2
- 3/2
- None of these
Explanation
To find the value of c that satisfies the Mean Value Theorem, we need to find the derivative of the function f(x) = x^2 + 2x + 1.
f'(x) = 2x + 2
The Mean Value Theorem states that there exists a point c in the interval [1, 2] such that:
f'(c) = (f(2) - f(1)) / (2 - 1)
First, let's calculate f(2) and f(1):
f(2) = 2^2 + 2(2) + 1 = 9
f(1) = 1^2 + 2(1) + 1 = 4
Now, we can calculate the slope:
(f(2) - f(1)) / (2 - 1) = (9 - 4) / 1 = 5
Now, we set f'(c) equal to 5:
2c + 2 = 5
Solving for c, we get:
2c = 3
c = 3/2
Since c = 3/2 is between 1 and 2, it satisfies the Mean Value Theorem.
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اس سوال کو وضاحت کے ساتھ پڑھیں
- Factoring the polynomial
- Finding the derivative
- Substituting the value of x
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- x = 2, −1/2
- x = 1, −2
- x = 3, −1
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- Commutative
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- Distributive
- None of these
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