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More with Rules for Differentiation

Learn how to evaluate derivatives, find the slope of a function, and determine equations of tangent lines. Practice exercises included.

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More with Rules for Differentiation

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  1. More with Rules for Differentiation Warm-Up: Find the derivative of f(x) = 3x2 – 4x4+1

  2. Objective • To evaluate a derivative at a point. • To use the derivative to find the slope of a function. • To use the derivative to find the equation of a tangent line. • TS: Making decisions after reflection and review.

  3. Evaluating Derivatives • Find the value of the derivative of:

  4. Evaluating Derivatives • Find the value of the derivative of:

  5. Tangent Lines • Find an equation of the tangent line to the graph of: Slope of the tangent line

  6. Tangent Lines Equation of the tangent line to f (x) at (3, 2)

  7. Tangent Lines • Find an equation of the tangent line to the graph of: Slope of the tangent line

  8. Tangent Lines Equation of the tangent line to f (x) at

  9. Slope of a Function Determine the point(s) at which the graph of has a slope of 1.

  10. Slope of a Function Points with a slope of 1

  11. Conclusion • To find an equation of a tangent line: • First, find the derivative of the function. • Next, plug the corresponding x-value into the derivative, to find the slope. • Finally, use the slope and the point to write an equation of the line.

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