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 f_x(2, 0) = 3, f_y(2, 0) = 2, f_xx(2, 0) = 4, f_yy(2, 0) = 3, and f_xy(2, 0) = 1.

h'(t) = f_x * 2e^t+ f_y

find h''(t) when t = 0.

(I don't understand how for the second partial derivative d/dy (f_y) = d/dt (x) *f_yx + d/dt(y) * f_yy

Could you explain this step for me in the solution. Thank you :)

Expert Solution

milcah answered 1 year ago

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

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...

If f and g are both differentiable functions. If h = f g, then h'(2) is: ___________________

If f and g are both differentiable functions. If h = f g, then h'(2) is: ___________________ Given the function: y=sin(4x)+e^-3x and dx/dt = 3 when x=0. Then dy/dt = ________________ when x=0. Let f(x) = ln (√x). The value of c in the interval (1,e) for which f(x) satisfies the Mean Value Theorem (i.e f'(c)= f(e)-f(1) / e-1 ) is: _________________________ Suppose f(x) is a piecewise function: f(x) = 3x^2 -11x-4, if x ≤ 4 and f(x) =...

Let f(t)=5t2−t. a) Find f(t+h): b) Find f(t+h)−f(t): c) Find f(t+h)−f(t)/h: side note: (f(t+h)=f(t) is on...

Let f(t)=5t2−t. a) Find f(t+h): b) Find f(t+h)−f(t): c) Find f(t+h)−f(t)/h: side note: (f(t+h)=f(t) is on top of fraction and h is on bottom) d) Find f′(t): pls circle the 4 answers

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

Let f be a continuous function on [a, b] which is differentiable on (a,b). Then f...

Let f be a continuous function on [a, b] which is differentiable on (a,b). Then f is non-decreasing on [a,b] if and only if f′(x) ≥ 0 for all x ∈ (a,b), while if f is non-increasing on [a,b] if and only if f′(x) ≤ 0 for all x ∈ (a, b). can you please prove this theorem? thank you!

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 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).

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

Question

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

Solutions

Expert Solution

Related Solutions

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

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

If f and g are both differentiable functions. If h = f g, then h'(2) is: ___________________

Let f(t)=5t2−t. a) Find f(t+h): b) Find f(t+h)−f(t): c) Find f(t+h)−f(t)/h: side note: (f(t+h)=f(t) is on...

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.

Let f be a continuous function on [a, b] which is differentiable on (a,b). Then f...

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

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

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