Use the graph of g to answer the questions below. AY g(k) to a) Carefully estimate g(-3) b) Very carefully sketch the tangent line to g when x=-3 c) Use (b.) and the graph to carefully estimate g'(-3) d) Is g continuous at x-3? Explain why or why not using the definition.

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A: Given: y= ex  The average slope of y = f(x) = ex on [0,1] (f(1) - f(0))/1-0 e1 - e0 =  e - 1 = 1.718…

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A: The slope of tangent to a curve y=f(x) at a point x=a is given by f'(a)

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A: Given: f'(x)=x3Tangent line to the given curve is:  4x-12y=3Therefore: y=8x-6

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A: According to chain rule of differentiation ddxfgx=f'gx·g'(x) . Now using this rule differentiate the…

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A: topic - derivative of a function using limits

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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: