1in q 3 it is (0<x<5)....find the interval in whichh g(x) is increasing
1) f is a continuous in [a,b] and differentiable in (a,b) wher a>0 such that f(a)/a = f(b)/b
prove that der exists x0 e (a,b) such that f'(x0)=f(x0)x0
2)find the value of a for which f(x)={3x+mod(a2-4) ,a≤x≤1
{5-x2 , x≥1
has the largest value at x=1
3)if f(x)=2x3-15x2+24x ang g(x)=\int_{0}^{x}{f(t)dt} + \int_{0}^{5-x}{f(t)dt} (0
-
UP 0 DOWN 0 0 7
7 Answers
1
11q2) is damn easy, first figure out for which range of a f(x) is continuous at x=1.....then try....
q3) is simple application of leibnitz rule, honey.
62for q1,
take g(x) =f(x)/x
g(a)=g(b)
g'(c) = 0 for some c in (a,b)
g'(x)=f'(x)/x - f(x)/x2 =0 (for some x0 in (a,b))
so f'(x) - f(x)/x =0 for some x0 in (a,b)