Question

Let g from R to R is a differentiable function, g(0)=1, g’(x)>=g(x) for all x>0 and...

Let g from R to R is a differentiable function, g(0)=1, g’(x)>=g(x) for all x>0 and g’(x)=<g(x) for all x<0. Proof that g(x)>=exp(x) for all x belong to R.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let f: R -> R and g: R -> R be differentiable, with g(x) ≠ 0...
Let f: R -> R and g: R -> R be differentiable, with g(x) ≠ 0 for all x. Assume that g(x) f'(x) = f(x) g'(x) for all x. Show that there is a real number c such that f(x) = cg(x) for all x. (Hint: Look at f/g.) Let g: [0, ∞) -> R, with g(x) = x2 for all x ≥ 0. Let L be the line tangent to the graph of g that passes through the point...
4a). Let g be continuous at x = 0. Show that f(x) = xg(x) is differentiable...
4a). Let g be continuous at x = 0. Show that f(x) = xg(x) is differentiable at x = 0 and f'(0) = g(0). 4b). Let f : (a,b) to R and p in (a,b). You may assume that f is differentiable on (a,b) and f ' is continuous at p. Show that f'(p) > 0 then there is delta > 0, such that f is strictly increasing on D(p,delta). Conclude that on D(p,delta) the function f has a differentiable...
Let f : R → R be a bounded differentiable function. Prove that for all ε...
Let f : R → R be a bounded differentiable function. Prove that for all ε > 0 there exists c ∈ R such that |f′(c)| < ε.
a) Let f : [a, b] −→ R and g : [a, b] −→ R be...
a) Let f : [a, b] −→ R and g : [a, b] −→ R be differentiable. Then f and g differ by a constant if and only if f ' (x) = g ' (x) for all x ∈ [a, b]. b) For c > 0, prove that the following equation does not have two solutions. x3− 3x + c = 0, 0 < x < 1 c) Let f : [a, b] → R be a differentiable function...
. Let f and g : [0, 1] → R be continuous, and assume f(x) =...
. Let f and g : [0, 1] → R be continuous, and assume f(x) = g(x) for all x < 1. Does this imply that f(1) = g(1)? Provide a proof or a counterexample.
If f is a differentiable function such that f′(x) = (x^2− 16)*g(x), where g(x)>0 for all...
If f is a differentiable function such that f′(x) = (x^2− 16)*g(x), where g(x)>0 for all x, at which value(s) of x does f have a local maximum? 1. At both x=-4,4 2. Only at x=-16 3. Only at x=4 4. At both x=-16,16 5. Only at x=-4 6. Only at x=16
Let f : E → R be a differentiable function where E = [a,b] or E...
Let f : E → R be a differentiable function where E = [a,b] or E = (−∞,∞), show that if f′(x) not = 0 for all x ∈ E then f is one-to-one, i.e., there does not exist distinct points x1,x2 ∈ E such that f(x1) = f(x2). Deduce that f(x) = 0 for at most one x.
Let f be a function differentiable on R (all real numbers). Let y1 and y2 be...
Let f be a function differentiable on R (all real numbers). Let y1 and y2 be pair of numbers (y1 < y2) with the property f(y1) = y2 and f(y2) = y1. Show there exists a num where the value of f' is -1. Name all theroms that you use and explain each step.
Let f: R --> R be a differentiable function such that f' is bounded. Show that...
Let f: R --> R be a differentiable function such that f' is bounded. Show that f is uniformly continuous.
Consider the function g(x) = |3x + 4|. (a) Is the function differentiable at x =...
Consider the function g(x) = |3x + 4|. (a) Is the function differentiable at x = 10? Find out using ARCs. If it is not differentiable there, you do not have to do anything else. If it is differentiable, write down the equation of the tangent line thru (10, g(10)). (b) Graph the function. Can you spot a point “a” such that the tangent line through (a, f(a)) does not exist? If yes, show using ARCS that g(x) is not...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT