Does knowing that a function f(x) is differentiable at x = x, tell you anything about the differentiability of the function -f at x = x,? Give reasons for your answer.phChoose the correct answer below.A. If a function f(x) is differentiable at x = X0, then - f(x) is not necessarily differentiable at x = Xo, because the slope of – f(x) is not known.B. If a function f(x) is differentiable at x = xo, then - f(x) is also differentiable at x = x0, because if it has a slope at x = Xp, it will have the negative of that slope whenit is reflected across the x-axis.O C. If a function f(x) is differentiable at x = X9, then - f(x) is not necessarily differentiable at x = x, because - f(x) is undefined.O D. If a function f(x) is differentiable at x = x,, then - f(x) is not necessarily differentiable at x = X; because lim - f(x) is not known.

A function f:ℝ→ℝ is differentiable at a point x∈ℝ if limh→0f(x+h)-f(x)h exists and we denote…

Does knowing that a function f(x) is differentiable at x = x, tell you anything about the differentiability of the function -fat x = x,? Give reasons for your answer. Choose the correct answer below. O A. If a function f(x) is differentiable at x = X0, then - f(x) is not necessarily differentiable at x = Xo, because the slope of - f(x) is not known. O B. If a function f(x) is differentiable at x = X, then - f(x) is also differentiable at x = xo, because if it has a slope at x = xo, it will have the negative of that slope when it is reflected across the x-axis. O C. If a function f(x) is differentiable at x = X0., then -f(x) is not necessarily differentiable at x = Xo, because - f(x) is undefined. O D. If a function f(x) is differentiable at x = x, then - f(x) is not necessarily differentiable at x = Xo, because lim - f(x) is not known.

Does knowing that a function f(x) is differentiable at x = x, tell you anything about the differentiability of the function -fat x = x,? Give reasons for your answer. Choose the correct answer below. O A. If a function f(x) is differentiable at x = X0, then - f(x) is not necessarily differentiable at x = Xo, because the slope of - f(x) is not known. O B. If a function f(x) is differentiable at x = X, then - f(x) is also differentiable at x = xo, because if it has a slope at x = xo, it will have the negative of that slope when it is reflected across the x-axis. O C. If a function f(x) is differentiable at x = X0., then -f(x) is not necessarily differentiable at x = Xo, because - f(x) is undefined. O D. If a function f(x) is differentiable at x = x, then - f(x) is not necessarily differentiable at x = Xo, because lim - f(x) is not known.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

Question

Does knowing that a function f(x) is differentiable at x = x, tell you anything about the differentiability of the function -f at x = x,? Give reasons for your answer.
ph
Choose the correct answer below.
A. If a function f(x) is differentiable at x = X0, then - f(x) is not necessarily differentiable at x = Xo, because the slope of – f(x) is not known.
B. If a function f(x) is differentiable at x = xo, then - f(x) is also differentiable at x = x0, because if it has a slope at x = Xp, it will have the negative of that slope when
it is reflected across the x-axis.
O C. If a function f(x) is differentiable at x = X9, then - f(x) is not necessarily differentiable at x = x, because - f(x) is undefined.
O D. If a function f(x) is differentiable at x = x,, then - f(x) is not necessarily differentiable at x = X; because lim - f(x) is not known.

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