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Suppose that functions f and g and their derivatives have the following values at x = 2 and x = 3. 2 3 8 3 2 –4 1/3–3 5 Evaluate the derivatives with.

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Presentation on theme: "Suppose that functions f and g and their derivatives have the following values at x = 2 and x = 3. 2 3 8 3 2 –4 1/3–3 5 Evaluate the derivatives with."— Presentation transcript:

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2 Suppose that functions f and g and their derivatives have the following values at x = 2 and x = –4 1/3–3 5 Evaluate the derivatives with respect to x of the following combinations at the given value of x. (a)at x = 2 At x = 2:

3 Suppose that functions f and g and their derivatives have the following values at x = 2 and x = –4 1/3–3 5 Evaluate the derivatives with respect to x of the following combinations at the given value of x. (b) at x = 3 At x = 3:

4 Suppose that functions f and g and their derivatives have the following values at x = 2 and x = –4 1/3–3 5 Evaluate the derivatives with respect to x of the following combinations at the given value of x. (c) at x = 3 At x = 3:

5 Suppose that functions f and g and their derivatives have the following values at x = 2 and x = –4 1/3–3 5 Evaluate the derivatives with respect to x of the following combinations at the given value of x. (d) at x = 2

6 Suppose that functions f and g and their derivatives have the following values at x = 2 and x = –4 1/3–3 5 Evaluate the derivatives with respect to x of the following combinations at the given value of x. (e) at x = 2

7 Suppose that functions f and g and their derivatives have the following values at x = 2 and x = –4 1/3–3 5 Evaluate the derivatives with respect to x of the following combinations at the given value of x. (f) at x = 2

8 Suppose that functions f and g and their derivatives have the following values at x = 2 and x = –4 1/3–3 5 Evaluate the derivatives with respect to x of the following combinations at the given value of x. (g) at x = 3

9 Suppose that functions f and g and their derivatives have the following values at x = 2 and x = –4 1/3–3 5 Evaluate the derivatives with respect to x of the following combinations at the given value of x. (h) at x = 2

10 Suppose that functions f and g and their derivatives have the following values at x = 2 and x = –4 1/3–3 5 Evaluate the derivatives with respect to x of the following combinations at the given value of x. (h) at x = 2

11 Slopes of Parametrized Curves Usually, we write this in a different form… A parametrized curve (x(t), y(t)) is differentiable at t if x and y are differentiable at t. At a point on a differentiable parametrized curve where y is also a differentiable function of x, the derivatives dy/dt, dx/dt, and dy/dx are related by the Chain Rule: If all three derivatives exist and,

12 Practice Problems Find the equation of the line tangent to the curve at the point defined by the given value of t. Find the three derivatives:

13 Find the equation of the line tangent to the curve at the point defined by the given value of t. The line passes through: And has slope: Equation of the tangent line:

14 Practice Problems Find the equation of the line tangent to the curve at the point defined by the given value of t. Derivatives: Point: Slope: Equation of the tangent line:


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