If f(a,b)`=(f(b)-f(a))/(b-a)` and
`f(a,b,c)=(f(b,c)-f(a,b))/(c-a)` prove that `f(a,b,c)=|{:(f(a),f(b),f(c)),(1,1,1),(a,b,c):}|-:|{:(1,1,1),(a,b,c),(a^(2),b^(2),c^(2)):}|`.

Find c so that f'(c)=(f(b)-f(a))/(b-a) " where " f(x)=e^(x), a=0, b=1

If f'(c)=(f (b)-f(a))/(b-a) , where f(x) =e^(x), a=0 and b=1 , then: c = ….

int_(a)^(b-a)f''(x+a)dx equals (a) f(b-a)-f(a) " " (b) f(b)-f(2a) (c) f'(b)-f'(2a) " " (d) f'(b-a)-f'(2a)

If a!=1, b!=1, c!=1, f(x)= 1/(1-x) and |(a,1,1),(1,b,1),(1,1,c)|=0 then (A) f(a)+f(b)+f(c)=0 (B) f(a)+f(b)+f(c)=1 (C) f(a)+f(b)+f(c)=-1 (D) f(a)f(b)f(c)=1

If g(x)=(f(x))/((x-a)(x-b)(x-c)), where f(x) is a polynomial of degree lt3, then prove that (dg(x))/(dx)=|{:(1,a,f(a)(x-a)^(-2)),(1,b,f(b)(x-b)^(-2)),(1,c,f(c)(x-c)^(-2)):} |divide|{:(a^(2),a,1),(b^(2),b,1),(c^(2),c,1):}|.

If f={(a, 1), (b, -2), (c, 3)}, g={(a, -2), (b, 0), (c, 1)} then f^(2)+g^(2)=

If f(x)<0,\ x in (a , b) then at the point C(c ,\ f(c)) on y=f(x) for which F(c) is a maximum, f^(prime)(c) is given by a. f^(prime)(c)=(f(b)-f(a))/(b-1) b. \ f^(prime)(c)=(f(b)-f(a))/(a-b) c. f^(prime)(c)=(2(f(b)-f(a)))/(b-a) d. f^(prime)(c)=0