" 13."(x+b)^(3)-a-b

In the mean value theorem f(b)-f(a)=(b-a)f'(c ), (a lt c lt b)," if " f(x)=x^(3)-3x-1 and a=-(11)/(7), b=(13)/(7) , find the value of c.

Find the value of a and b so that the polynomial x^(3)-ax^(2)-13x+b has (x-1) and (x+3) as factors.

The values of a and b so that the polynomial x^(3)-ax^(2)-13x+b has (x-1) and (x+3) as factors respectively are

If (9x-13)/(x^(2)-2x-15)=(A)/(x+3)+(B)/(x-5) , then A+B is ________.

If (x)/(a)=(y)/(b)=(z)/(c) , then prove that each ratio is equal to ((3x^(3)-11y^(3)+13z^(3))/(3a^(3)-11b^(3)+13c^(3)))^((1)/(3))

The function f(x)=x^(3)-6x^(2)+ax+b satisfy the conditions of Rolle's theorem in [1,3] .The values of a and b are

If f(x) = 2x^(4) - 13x^(2) + ax + b is divisible by x^(2) - 3x + 2, then (a,b) =

If a:b=2:5, then (3a+2b)/(4a+b)=(16)/(13)( b) (13)/(16)(25)/(22)(d)(20)/(21)

If the 7th and 8th term of the binomial expansion (2a - 3b)^(n) are equal, then (2a +3b)/(2a-3b) is equal to a) (13-n)/-(n+1) b) (n+1)/(13-n) c) (6-n)/(13-n) d) (n-1)/(13-n)

Verify Mean Value theorem, if f(x)=x^(3)-5x^(2)-3x in the interval [a, b], where a = 1 and b = 3. Find all cin(1,3) for which f'( c) = 0.