Advertisements
Advertisements
Question
The value of c in Mean value theorem for the function f(x) = x(x – 2), x ∈ [1, 2] is ______.
Options
`3/2`
`2/3`
`1/2`
`3/2`
Solution
The value of c in Mean value theorem for the function f(x) = x(x – 2), x ∈ [1, 2] is `3/2`.
APPEARS IN
RELATED QUESTIONS
Verify Rolle's theorem for the function
f(x)=x2-5x+9 on [1,4]
Verify Rolle’s theorem for the function f (x) = x2 + 2x – 8, x ∈ [– 4, 2].
Verify Mean Value Theorem, if f (x) = x2 – 4x – 3 in the interval [a, b], where a = 1 and b = 4.
f(x) = (x-1)(x-2)(x-3) , x ε[0,4], find if 'c' LMVT can be applied
Verify Rolle’s Theorem for the function f(x) = ex (sin x – cos x) on `[ (π)/(4), (5π)/(4)]`.
Verify Mean value theorem for the function f(x) = 2sin x + sin 2x on [0, π].
Verify mean value theorem for the function f(x) = (x – 3)(x – 6)(x – 9) in [3, 5].
f(x) = `sin^4x + cos^4x` in `[0, pi/2]`
Using Rolle’s theorem, find the point on the curve y = x(x – 4), x ∈ [0, 4], where the tangent is parallel to x-axis
f(x) = `1/(4x - 1)` in [1, 4]
f(x) = x3 – 2x2 – x + 3 in [0, 1]
f(x) = `sqrt(25 - x^2)` in [1, 5]
Find a point on the curve y = (x – 3)2, where the tangent is parallel to the chord joining the points (3, 0) and (4, 1)
Using mean value theorem, prove that there is a point on the curve y = 2x2 – 5x + 3 between the points A(1, 0) and B(2, 1), where tangent is parallel to the chord AB. Also, find that point
For the function f(x) = `x + 1/x`, x ∈ [1, 3], the value of c for mean value theorem is ______.
If x2 + y2 = 1, then ____________.
The value of c in Rolle’s theorem for the function, f(x) = sin 2x in `[0, pi/2]` is ____________.
If the greatest height attained by a projectile be equal to the horizontal range, then the angle of projection is
If A, G, H are arithmetic, geometric and harmonic means between a and b respectively, then A, G, H are
Value of' 'c' of the mean value theorem for the function `f(x) = x(x - 2)`, when a = 0, b = 3/2, is
If `1/(a + ω) + 1/(b + ω) + 1/(c + ω) + 1/(d + ω) = 1/ω`, where a, b, c, d ∈ R and ω is a cube root of unity then `sum 3/(a^2 - a + 1)` is equal to
Rolle's Theorem holds for the function x3 + bx2 + cx, 1 ≤ x ≤ 2 at the point `4/3`, the value of b and c are
P(x) be a polynomial satisfying P(x) – 2P'(x) = 3x3 – 27x2 + 38x + 1.
If function
f(x) = `{{:((P^n(x) + 18)/6, x ≠ π/2),(sin^-1(ab) + cos^-1(a + b - 3ab), x = π/2):}`
is continuous at x = ` π/2`, then (a + b) is equal to ______.
