As xx varies from −1 to +3, which one of the following describes the behaviour of the function f(x) = x3–3x2 + 1?
Given the following statements about a function f : R→R, select the right option:
P: If f(x) is continuous at x = x0, then it is also differentiable at x = x0
Q: If f(x) is continuous at x = x0, then it may not be differentiable at x = x0
R: If f(x) is differentiable at x = x0, then it is also continuous at x = x0
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Given f(x) = x3 + ax2 + bx + c and y-intercept for the function is 1. Also f has local extrema at x = -4 and x = 2. Then a + b + c = ____
Find C of Rolle’s theorem for f(x) = ex(sin x - cos x) in
If f(x) is differentiable and g’(x) ≠ 0 such that f(1) = 4, f(2) = 16, f’(x)= 8g’(x) and g(2) = 4 then what is the value of g(1) ?
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What are the minimum and maximum value of the below-given function respectively?
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If f(x) = x3 − 3x−1 is continuous in the closed interval and f’(x) exists in the open interval then find the value of c such that it lies in
Find the maximum and minimum values of f(x) = sin x + cos 2x where 0≤ x ≤2π
55 docs|215 tests
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55 docs|215 tests
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