Let c E R. Let g be a function with domain R. We know the following: g(0) = 0 • g is differentiable at 0 and g (0) = c %3D • for every x, y ER, g(x+y) = g(x) +2xy+ g(y). Prove that g is differentiable everywhere and find a formula for g'.

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A: solution:- a)  To find the derivative of f(x)

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A: Topic:- application of derivatives

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A:

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A: Step 1: Step 2:Step 3:Step 4:

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A: I have explained everything with in the solution. Please go through that.

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Q: The graph of f', the derivative of f, is shown below. Determine the values of x, if any, at which…

A:

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: