DERIVATIVES
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1. If f(x) = 2x + 3, use the definition of derivative
to find and then enter the rule for the derivative at x = a:
2.
By using the definition of derivative, find and enter the derivative
at x = 1 (numerator followed by denominator).
Sketch the graph and show the tangent line at x = 1.
3. Using the derivative rules, find and enter the slope of the tangent
line at x = 1 if f(x) = x2 + 2x +5. Sketch the graph and the tangent line on the same axes.
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4. If f(x) = |
1 + x2
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find the slope of the tangent line at (1, |
1
2
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5. If y = |
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1
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Find y ¢(1) |
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6. At what point in Quadrant I is the line 3x + y = 0 parallel to a tangent
line to xy = 12? Enter the point in the form
(a,b). Sketch the graph and the tangent line.
7.
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Find y ¢(-1) if y = xex-1 |
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8. Let y(x) = ln|cos2x| for 0 £ x £ p. Find y ¢( |
p
2
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9. First, find the 2d derivative of y = e-tsint. Is it true that y ¢¢+ 2y ¢+ 2y = 0? |
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