By Christopher Thomas
Updated on Oct 1, 2011
To review these concepts, go to Derivatives Study Guide.
Derivatives Practice Questions
- Find the derivative of f(x) = 8x + 2.
- If h(x) = x^{2} + 5, then what is h'(x)?
- Find the derivative of g(x) = 10.
- What is the derivative of g(x) = 3 –5x?
- Find the derivative of f(x) = 3√x.
- If k(x) = x^{3}, then what is k'(x)?
- Find the slope of f(x) = 3x^{2} + x at x = 2.
- Where does the graph of g(x) = x^{2} – 4x + 1 have a slope of 0?
- Find the equation of the tangent line to h(x) =1 – x^{2} at (2,–3).
- What is the equation of the tangent line of k(x) = 5x^{2} + 2x at x= 1?
Solutions
- Thus, at x = 2, the slope is f'(2) = 13
- Thus, there is a slope of zero when g'(x) = 2x – 4 = 0, This happens when x = 2,
- The slope at (2,–3) is h'(2) = –4, so the equation of the tangent line is y = –4(x – 2) – 3 = –4x + 5.
- The y value at x = 1 is k (1) = 7.The slope at x = 1 is k'(1) = 12. The equation of the tangent line is y = 12(x– 1) + 7 = 12x – 5.
From Calculus Success in 20 Minutes A Day. Copyright © 2006 by LearningExpress, LLC. All Rights Reserved.
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