What is the equation of the tangent line at $$x = 1$$ for the function $$f(x) = \, \text{sqrt}(x)$$ ?

The equation of the tangent line is $$y = \frac{1}{2}x + \frac{1}{2}$$ .

What is the equation of the line tangent to the curve $$y = x^2$$ at $$x = 1$$ ?

The equation of the tangent line is $$y = 2x - 1$$ .

Find the equation of the normal line at $$x = 0$$ for the function $$f(x) = x^3 + e^x$$ .

The equation of the normal line is $$y = -x + 1$$ .

What is the quotient rule for derivatives?

If $$u(x)$$ and $$v(x)$$ are functions, then $$(u/v)$$ .

What is the chain rule for derivatives?

If $$y = f(g(x))$$ , then $$dy/dx = f$$ .

How do you find the slope of the tangent line at a point?

The slope of the tangent line at a point is given by the derivative of the function evaluated at that point.

What is the significance of the normal line in relation to the tangent line?

The normal line is perpendicular to the tangent line at the point of tangency.

What is the formula for the equation of a line given a point and a slope?

The equation of the line is given by $$y - y_1 = m(x - x_1)$$ , where $$m$$ is the slope and $$(x_1, y_1)$$ is the point.

What is the second derivative and its significance?

The second derivative is the derivative of the derivative, and it indicates the concavity of the function.

Calculus Review: Derivatives and Equation of Tangent and Normals Flashcards

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5.

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6.

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What is the definition of a derivative?

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The derivative of a function at a point is the limit of the average rate of change of the function as the interval approaches zero.

7.

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What is the product rule for derivatives?

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