Suppose f is a twice differentiable function such that f′(x)>0 and f′′(x)<0 everywhere, and consider the...

Suppose f is a twice differentiable function such that f′(x)>0 and f′′(x)<0 everywhere, and consider the following data table.

x 0 1 2

f(x) 3 A B

For each part below, determine whether the given values of A and B are possible (i.e., consistent with the information about f′and f′′ given above) or impossible, and explain your answer.

a)A= 5, B= 6

(b)A= 5, B= 8

(c)A= 6, B= 6

(d)A= 6, B= 6.1

(e)A= 6, B= 9

Expert Solution

milcah answered 2 years ago

Consider a continuous, integrable, twice-differentiable function f with input variable x. In terms of the units...

Consider a continuous, integrable, twice-differentiable function f with input variable x. In terms of the units of f and the units of x, choose the units of each function or expression below: (a) The units of f ' are the units of f the units of x (the units of f)(the units of x ) the units of f the units of x the units of f (the units of x)2 the units of f (the units...

1) Let f(x) be a continuous, everywhere differentiable function and g(x) be its derivative. If f(c)...

1) Let f(x) be a continuous, everywhere differentiable function and g(x) be its derivative. If f(c) = n and g(c) = d, write the equation of the tangent line at x = c using only the variables y, x, c, n, and d. You may use point-slope or slope-intercept but do not introduce more variables. 2) Let f(x) be a continuous, everywhere differentiable function. What kind information does f'(x) provide regarding f(x)? 3) Let f(x) be a continuous, everywhere differentiable...

Suppose that f is a differentiable function with derivative f" (x) = (x − 3)(x +...

Suppose that f is a differentiable function with derivative f" (x) = (x − 3)(x + 1)(x + 5). Determine the intervals of x for which the function of f is increasing and decreasing Explain why a positive value for f" (x) means the graph f(x) is increasing For f(x) = 2x2- − 3x2 − 12x + 21, find where f'(x) = 0, and the intervals on which the function increases and decreases Determine the values of a, b, and...

Let f : Rn → R be a differentiable function. Suppose that a point x∗ is...

Let f : Rn → R be a differentiable function. Suppose that a point x∗ is a local minimum of f along every line passes through x∗; that is, the function g(α) = f(x^∗ + αd) is minimized at α = 0 for all d ∈ R^n. (i) Show that ∇f(x∗) = 0. (ii) Show by example that x^∗ neen not be a local minimum of f. Hint: Consider the function of two variables f(y, z) = (z − py^2)(z...

f is a twice differentiable function and that itssecond partial derivatives are continuous.Let h(t)...

f is a twice differentiable function and that its second partial derivatives are continuous. Let h(t) = f (x(t), y(t)) where x = 2e t and y = t. Suppose that fx(2, 0) = 3, fy(2, 0) = 2, fxx(2, 0) = 4, fyy(2, 0) = 3, and fxy(2, 0) = 1. h'(t) = fx * 2e t+ fy find h''(t) when t = 0. (I don't understand how for the second partial derivative d/dy (fy) = d/dt (x) *fyx...

Suppose f(x) is a very well behaved function in that it is continuous and differential everywhere,...

Suppose f(x) is a very well behaved function in that it is continuous and differential everywhere, and that f(2) = 6 and f(6) = 34. a. Find the slope of the line between these two points on the graph. b. What does the Mean Value Theorem tell you about f(x) in the interval between x = 2, and x = 6?

At what point is the function f(x)= |3-x| not differentiable.

Let f be a differentiable function on the interval [0, 2π] with derivative f' . Show...

Let f be a differentiable function on the interval [0, 2π] with derivative f' . Show that there exists a point c ∈ (0, 2π) such that cos(c)f(c) + sin(c)f'(c) = 2 sin(c).

For the following exercises, consider the graph of the function f and determine where the function is continuous/ discontinuous and differentiable/not differentiable.

Question

Suppose f is a twice differentiable function such that f′(x)>0 and f′′(x)<0 everywhere, and consider the...

Solutions

Expert Solution

Related Solutions

Consider a continuous, integrable, twice-differentiable function f with input variable x. In terms of the units...

1) Let f(x) be a continuous, everywhere differentiable function and g(x) be its derivative. If f(c)...

Suppose that f is a differentiable function with derivative f" (x) = (x − 3)(x +...

Let f : Rn → R be a differentiable function. Suppose that a point x∗ is...

f is a twice differentiable function and that itssecond partial derivatives are continuous.Let h(t)...

Suppose f(x) is a very well behaved function in that it is continuous and differential everywhere,...

At what point is the function f(x)= |3-x| not differentiable.

Let f be a differentiable function on the interval [0, 2π] with derivative f' . Show...

For the following exercises, consider the graph of the function f and determine where the function is continuous/ discontinuous and differentiable/not differentiable.

For the following exercises, consider the graph of the function f and determine where the function is continuous/ discontinuous and differentiable/not differentiable.