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Solved Examples
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eee Use Rolle's Theorem to determine the value of c such that f ′ (c) = 0, if f(x) = x2 - 16x + 63 in the interval [7, 9]. eee View Solution
eee Use Rolle's Theorem to determine the value of c such that f ′ (c) = 0, if f(x) = x(x + 3) e-x2 in the interval [- 3, 0].
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eee Use Rolle's Theorem to determine the value of c such that f ′(c) = 0, if f(x) = log (x2+12-2x) in the interval [- 4, - 3].
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eee Use Rolle's Theorem to determine the value of c such that f ′ (c) = 0, if f(x) = cos x in the interval [- π2, π2].
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eee Use Rolle's Theorem to determine the value of c such that f ′ (c) = 0, if f(x) = (x - a)m (x - b)n where m, n are positive integers in the interval [a, b]. eee View Solution
eee Find the value in the interval, which satisfies the Mean Value Theorem for the function f(x) = x - x3 on [- 2, 1].
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eee Find the value in the interval, which satisfies the Mean Value Theorem for the function f(x) = 4x3 - 5x2 + x - 2 on [0, 1]. eee View Solution
eee Find the value in the interval, which satisfies the Mean Value Theorem for the function f(x) = ln x on [1, e]. eee View Solution
eee Find the value in the interval, which satisfies the Mean Value Theorem for the function f(x) = x43 on [- 1, 1]. eee View Solution
eee Find the value in the interval, which satisfies the Mean Value Theorem for the function f(x) = 1-x on [- 8, 1]. eee View Solution
eee Use Rolle's Theorem to determine the value of c such that f ′ (c) = 0, if f(x) = xx+5 in the interval [- 5, 0].
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eee Use Rolle's Theorem to determine the value of c such that f ′ (c) = 0, if f(x) = x2-4x-12x+4 in the interval [- 2, 6].
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eee Use Rolle's Theorem to determine the value of c such that f ′ (c) = 0, if f(x) = (x + 3)(x - 1)2 in the interval [- 3, 1]. eee View Solution
eee Use Rolle's Theorem to determine the value of c such that f ′ (c) = 0, if f(x) = 1 - x2 in the interval [- 1, 1].
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eee Use Rolle's Theorem to determine the value of c such that f ′ (c) = 0, if f(x) = x(x - 1) in the interval [0, 1].
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eee Use Rolle's Theorem to determine the value of c such that f ′ (c) = 0, if f(x) = x2 - 1 in the interval [- 1, 1].
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eee Find the value in the interval, which satisfies the Mean Value Theorem for the function f(x) = x(x2 - 2x - 3) on [- 1, 2]. eee View Solution
eee Find the value in the interval, which satisfies the Mean Value Theorem for the function f(x) = x+22x on [12, 2].
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eee Use Rolle's Theorem to determine the value of c such that f ′(c) = 0, if f(x) = sin 2x in the interval [0, 3π2].
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eee Find the value in the interval, which satisfies the Mean Value Theorem for the function f(x) = 1 + 1x on [1, 4]. eee View Solution
eee Find the value in the interval, which satisfies the Mean Value Theorem for the function f(x) = x2 - 4x on [2, 4]. eee View Solution
eee Find the value in the interval, which satisfies the Mean Value Theorem for the function f(x) = ax2 + bx + c on [l, m].
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eee Find the value in the interval, which satisfies the Mean Value Theorem for the function f(x) = (x - 1)(x - 2) on [0, 4].
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eee Find the value in the interval, which satisfies the Mean Value Theorem for the function f(x) = 2 + x3 on [- 1, 2].
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eee Find the value in the interval, which satisfies the Mean Value Theorem for the function f(x) = x2-9 on [3, 9]. eee View Solution