Is the following statement true or false? The function g(x) = x|x| has a derivative at x = 1. Choose the correct answer below. A. True. O B. False, since the function is not continuous at x = 1, it is not differentiable at x = 1. C. False, since the limit from the left and the limit from the right are not equal, the derivative does not exist. D. False, while a tangent line can be drawn at x = 1, it is vertical, meaning that the derivative does not exist.

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A: Given,                  y= f(x)                      (1)

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A: given                  f(x)=4x+7

Q: 6-Iff is a continuous at x=c, then f has a derivative at x=c. * a. True b. False

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Q: If h = z- x, which of the following best describes the derivative of f at x? I. limp0 f(z+h)-f(x)…

A: Solution:

Q: Hiwofind the derivative of the function fwith respect to Vaniable t,, tz when ti-l, tz=3 2. X=Lncti)

A:

Q: Define the derivative f'(a) of a function f at x =a.

A: To define: The derivative f'(a) of a function f(x) at x=a

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A:

Q: Fill in the blank/s:

A: We have to fill in the blank.

Q: (b) y = tan x

A: Use limit method of derivative

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Q: f(x) = 3-x/2x+

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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: