Suppose that f(x) is differentiable function such that f(1)=3 and f(1)=4. If g(x)= f(x) -, then what is gʻ(1)? x +1

Q: Compute the derivative of f (x) = x 3/2 using the limit definition.

A: fx=x32

Q: Is there a real function f(x) that is differentiable only at a point x?

A:

Q: Given the equation y In (x* +y - = 5, evaluate Assume that the equation implicitly defines y as a…

A: Given that, ylnx4+y4+1=5            ...(1)

Q: Use the first derivatives test to find local exterma of f( x) =x3 -12x on R

A:

Q: If y = f(x) is an odd differentiable function defined on (-o, 0) such that %3D f'(3) = -2 then…

A: A function f(x) is said to be even if f(-x) = f(x) And odd if f(-x) = -f(x)

Q: Prove that y = x- 2 is differentiable and calculate y'.

A: Given: The function, y = x-2

Q: if f(x) is a function that is continous at (2,f(x)) then f(x) is differentiable at (2,F(2))   true…

A: Given statement is If f(x) is a function that is continous at (2,f(x)) then f(x) is differentiable…

Q: Suppose that z = f(x, y) is implicitly defined as a function of x and y. Determine for 4x²z³ - 5yz²…

A:

Q: What is the minimum f(x) value of f(x) = sin x on the interval [0, 2]? %3!

A: Derivative Test: find values of x for which f'(x)=0 Then find f''(x) and put values pf x from above…

Q: Define a function f : R² → R² by f 2.у 1. Show that f is differentiable on A = E R² |x > 0, y > 0}…

A: To show that the function f defined as below is differentiable on A and compute its derivative

Q: Compute the derivative of f (x) = x 1/3 using the limit definition.                            (x +…

A: Given: fx=x13 To Find: The derivative of the given function using limit definition

Q: Suppose that flx) is a differentiable function and g(x)=(x+2)/f(x). If f(0)= 22 and f(0)=5, then…

A:

Q: Show that the function is differentiable by finding values of ε1 and ε2 as designated in the…

A: Given  f(x,y)=x2y

Q: Suppose that a firm uses L as an input, and its production function changes with L and a parameter…

A: Let’s apply the above approach to an economic application, namely the profit function of a…

Q: Show analytically that the function f is not differentiable at x = 0. Ax) = 2x+1 x>1

A:

Q: Prove that constant function is differentiable at ever x ER.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Show that f(x) = x – cos(x) has only 1 real zero on the interval [0, .

A: given fx=x-cosxx∈0,π2

Q: Assume that f is a function with domain [0,1] that is differentiable in (0,1). Assuming that f (0) =…

A:

Q: Show that if the graph of a twice-differentiable function ƒ(x) has an inflection point at x = a,…

A: Find the reason why the tangents lines fit well at the inflation points

Q: 11. Prove from the definition that the following functions are differentiable. ()- (b) f =xy?

A: By the definition, the function f(x,y)=xy^2 is differentiable if fx(x,y) and fy(x,y) both exist.

Q: Find a positive value, c, for x, thot satisfies the Mean valve Theorem for derivatives for…

A:

Q: 10. Show that f (x) = { x² sin(1/x) if x + 0 if x is differentiable, but the derivative is not…

A:

Q: If f(2) is a continuous function at a point z, , then f(z) is differentiable at z, . But the…

A: Authoring guidelines:…

Q: Suppose f and g are differentiable functions on R such that, (x²+1)f (x) + 3xf(x) = e*2 + 7x and…

A:

Q: Let 'f be a continuously differentiable real valued function defined bx+a x<1 by f(x) = 5x² Then the…

A:

Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 16/x on the interval [0,…

A:

Q: Show that the function f(x) = exp(-|x|) is not differentiable at x = 0.

A: Given function is  fx=e-x given point is x=0.

Q: let f(x)= 5x2. Show that f(3+h)=5h2+30h+45. Then show that  (f(3+h)-f(3))/h=5h+30 and compute the…

A: Compute: f(3+h)

Q: Obtain the first and second derivative of the following real-valued functions 1. ƒ : R → R, such…

A: Solution :1.fx=23x3-2xfirst derivative ,f'xf'x=29x2-2Second derivative…

Q: Suppose that f: R² R is a function given by y³ x² + y² f(x, y) = 0 for x = y = 0. Show that f(x, y)…

A:

Q: Find all points (x.y) where f(x.y) has a possible relative maximum or minimum. Then use the second…

A: Given f(x,y)=x3-y2-48x+8y

Q: 4. Use the limit definition of derivative to find f'(x) for f(x) = V5x + 1. You will only get credit…

A:

Q: (b) Show that the function defined by √₂²+y f(x, y) = 0 if (x, y) = (0,0) is not differentiable at…

A: On solving this we will get

Q: 4. By the definition of derivative prove that f(x) = √x² +5 is differen- tiable at x=2.

A:

Q: Let [x² + 1 _ if x 1 f(x) - Is f differentiable at 1?:

A:

Q: Show that f(x) := x/3, x e R, is not differentiable at x 0.

A:

Q: Suppose f is differentiable with f(0) = 0 and 0 0.

A:

Q: Suppose that f(x)=xu(x), where u(x) is a differentiable function at x=2 such that u(2)=3, u'(2)=1.…

A:

Q: Show that x³, if x 0 is not continuous at x = 0. %3D

A: According to the problem, we have

Q: Use the First Derivative Test to classify each critical point of f(x) = x^4 − 8x^2 + 3 as a local…

A:

Q: Show that the function is differentiable by finding values of ε1 and ε2 as designated in the…

A: Given function is fx,y=x2+y2.…

Q: Suppose that a function f(x, y) satisfies fxx fyy – (fxy)² > 0 at a point (a, b). How is the sign of…

A:

Q: suppose the derivative of f exists, and assume that f(2)=3, f'(2)=4. Let g(x)=x^2f(x) and h(x)=…

A: The objective is to find the equation of tangent lines of g(x) and h(x) at x=2

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.