Let f be a differentiable function such that f(1) = 2 and f'(x) = f (x) for all x in R . If h(x)=f(f(x)), then h'(1) is equal to
Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then
Let f: R->R be a twice differentiable function such that f(x+pi)=f(x) and f''(x)+f(x)geq0 for all x in Rdot Show that f(x)geq0 for all x in Rdot
Let f: R->R and g: R->R be two non-constant differentiable functions. If f^(prime)(x)=(e^((f(x)-g(x))))g^(prime)(x) for all x in R , and f(1)=g(2)=1 , then which of the following statement(s) is (are) TRUE? f(2) 1-(log)_e2 (c) g(1)>1-(log)_e2 (d) g(1)<1-(log)_e2
If f:R->R is a twice differentiable function such that f''(x) > 0 for all x in R, and f(1/2)=1/2. f(1)=1, then
Let F : R to R be a thrice differentiable function . Suppose that F(1)=0,F(3)=-4 and F(x) lt 0 " for all" x in (1/2,3). f(x) = x F(x) for all x inR . The correct statement (s) is / are
Let f be a differentiable function from R to R such that abs(f(x)-f(y))abs(le2)abs(x-y)^(3//2) ,for all x,y inR .If f(0)=1 ,then int_(0)^(1)f^2(x)dx is equal to
Let f:R rarr(0,oo) and g:R rarr R be twice differntiable function such that f'' and g'' ar continous fucntion on R. Suppose f(2)=g(2)=0,f''(2)ne0and g''(2)ne0.If lim_(xrarr2) (f(X)g(x))/(f'(x)g'(x))=1 then
Let f: R rarr R be a differentiable function satisfying f(x+y)=f(x)+f(y)+x^(2)y+xy^(2) for all real numbers x and y. If lim_(xrarr0) (f(x))/(x)=1, then The value of f'(3) is
Let f: R->R be a differentiable function with f(0)=1 and satisfying the equation f(x+y)=f(x)f^(prime)(y)+f^(prime)(x)f(y) for all x ,\ y in R . Then, the value of (log)_e(f(4)) is _______
CENGAGE-DIFFERENTIATION-Multiple Correct Answers Type
