Questions from Calculus


Q: Find the derivatives from the left and from the right at x

Find the derivatives from the left and from the right at x = 1 (if they exist). Is the function differentiable at x = 1? f(x) = √1 – x2

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Q: Find the derivatives from the left and from the right at x

Find the derivatives from the left and from the right at x = 1 (if they exist). Is the function differentiable at x = 1?

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Q: Find the slope of the tangent line to the graph of the

Find the slope of the tangent line to the graph of the function at the given point. f(x) = 5 − x2 , (3, −4)

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Q: Find the derivatives from the left and from the right at x

Find the derivatives from the left and from the right at x = 1 (if they exist). Is the function differentiable at x = 1? f(x) = (1 − x)2/3

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Q: Determine whether the function is differentiable at x = 2.

Determine whether the function is differentiable at x = 2.

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Q: Determine whether the function is differentiable at x = 2.

Determine whether the function is differentiable at x = 2.

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Q: A line with slope m passes through the point (0,

A line with slope m passes through the point (0, 4) and has the equation y = mx + 4. a. Write the distance d between the line and the point (3, 1) as a function of m. b. Use a graphing utility to grap...

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Q: Consider the functions f(x) = x2 and g(

Consider the functions f(x) = x2 and g(x) = x3. a. Graph f and f′ on the same set of axes. b. Graph g and g′ on the same set of axes. c. Identify a pattern between f and g and their respective derivat...

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Q: If it is false, explain why or give an example that

If it is false, explain why or give an example that shows it is false. The slope of the tangent line to the differentiable function f at the point (2, f(2)) is f(2 + ∆x) - f (2) / ∆x.

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Q: If a function is continuous at a point, then it is

If a function is continuous at a point, then it is differentiable at that point.

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