Let h be a twice continuosly differentiable positive function on an open interval H. Let `g(x)=log_(e)(h(x))` for each `x in H`
Suppose `(h'(x))^(2)gt h''(x)h(x)` for each `x in H.`
Then, we can conclude that

Let h be a twice continuously differentiable positive function on an open interval J. Let g(x) = ln(h(x) for each x in J Suppose (h'(x))^2 > h''(x)h(x) for each x in J . Then

Let f(x) be continuous and differentiable function for all reals and f(x + y) = f(x) - 3xy + ff(y). If lim_(h to 0)(f(h))/(h) = 7 , then the value of f'(x) is

Let f be a twice differentiable function such that f^(prime prime)(x)=-f(x),a n df^(prime)(x)=g(x),h(x)=[f(x)]^2+[g(x)]^2dot Find h(10)ifh(5)=11

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:R to R and h:R to R be differentiable functions such that f(x)=x^(3)+3x+2,g(f(x))=x and h(g(g(x)))=x for all x in R . Then, h'(1) equals.

Let f:R to R and h:R to R be differentiable functions such that f(x)=x^(3)+3x+2,g(f(x))=x and h(g(x))=x for all x in R . Then, h'(1) equals.

Let f:R to R and h:R to R be differentiable functions such that f(x)=x^(3)+3x+2,g(f(x))=x and h(g(x))=x for all x in R . Then, h'(1) equals.

Let g: R -> R be a differentiable function with g(0) = 0,,g'(1)!=0 .Let f(x)={x/|x|g(x), 0 !=0 and 0,x=0 and h(x)=e^(|x|) for all x in R . Let (foh)(x) denote f(h(x)) and (hof)(x) denote h(f(x)) . Then which of the following is (are) true? A. f is differentiable at x = 0 B. h is differentiable at x = 0 C. f o h is differentiable at x = 0 D. h o f is differentiable at x = 0

Let f be a twice differentiable function such that f''(x)gt 0 AA x in R . Let h(x) is defined by h(x)=f(sin^(2)x)+f(cos^(2)x) where |x|lt (pi)/(2) . The number of critical points of h(x) are

Let h (x) = min (x, x^2), x in R , then h (x) is