5. Let f: R→ R is a differentiable function at to and f(xo) = 0. Show that if g(x) differentiable at ro, then f'(xo) = 0. f(x) is

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A: (i.) Given: A differentiable function, V:ℝ2→ℝ The function x:ℝ→ℝ2 satisfies the equation ddtxt=-∇Vxt…

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A: f:a, b→ℝ is differentiable.

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A: Consider the conditions for the mean value theorem.

Q: Let A E R"Xn, let b e R", and let n n f (x) = xT Ar + 6Tx = Aikr;xk +> b;x;. i,k=1 i=1 Show that f :…

A: Definition: A function f:ℝn→ℝm is differentiable at x0 with derivative M if M:ℝn→ℝm is linear and…

Q: Let y=f(X) defines a twice-differentiable function and let y=T(x) be the line tangent to the graph…

A:

Q: Consider the functions f(t) = e' and g(t) -81 defined on 0 st<o. %3D = e (a) (f* g)(t) can be…

A: Consider the functions, f(t) = et and g(t) = e-8t

Q: Let f (x, y) and g(x, y) be functions of two variables withthe property that ∂ f/∂x= ∂g/∂x and ∂…

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Q: Is there a twice differentiable function f R2R whose best adratic approximation at the point (1,0)…

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Q: 6. Let f(x) be a twice differentiable function with f(1) = 2, f(4) = 7, f'(1) = 5 and f'(4) = 3.…

A:

Q: Let f(x) be a differentiable function. Explain why it is possible that f'(c)=0 for a function but…

A: Let f(x) be a differentiable function.

Q: Let f be a function that is defined and differentiable on all of R. Here is some information about /…

A:

Q: Let f :R→R be a differentiable function, such that the secant line through any two points on its…

A: Let f: ℝ →ℝbe a differentiable function such that secant line through any two points on its graph…

Q: Check that the equation x³ + y³ + 2³ = x + y + z implicitly defines at least one differentiable…

A:

Q: Find the linear approximation to the function f(x, y) = sin y --- |T at x, = (1, -2) 2 and use it to…

A: The solution is given as

Q: u(0) = 3 and u(0) = -2. %3D Find the tangent line to the curve sin(zy) = -7u(x)y + 21. at the point…

A:

Q: Let f be a differentiable function with f(1) = -3, f'(1) =0, and 1+ f(x) h(x) = What is h' (1)?…

A:

Q: Let F(u, v) be a function of two variables. Let F,(u, v) = G(u, v), and F,(u, v) = H(u, v). Find f'…

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A: This question related to derivative.

Q: 1. Assume that f, g: RR are differentiable, f(0) = 3, f'(0) = 2, g(3) = 7 and g'(3) 4. Compute (go…

A: The answer is,Explanation:Consider,used formula: The composite function is,(g∘f)(x)=g(f(x))Take…

Q: Suppose f: IR→ R is a differentiable function. True or false: If f' (the derivative of f) is…

A: Solution :-true

Q: Let y = f(x) be implicitly defined by xsin y = ycos x. Compute y' in terms of x and y.

A: