Chapter 7

Basic Applications of the Derivative

Educators


Problem 1

Find the equation of the tangent to the graph of $y=3 x^{2}-x$ at $x=1$

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Problem 2

Find the equation of the tangent to the graph of $y=x^{3}-3 x$ at $x=3$

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Problem 3

Find the equation of the tangent to the graph of $y=\frac{1}{\sqrt{x^{2}+7}}$ at $x=3$

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Problem 4

Find the equation of the normal to the graph of $y=\frac{x+3}{x-3}$ at $x=4$

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Problem 5

Find the equation of the tangent to the graph of $y=2 x^{3}-3 x^{2}-12 x+20$ at $x=2$

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Problem 6

Find the equation of the tangent to the graph of $y=\frac{x^{2}+4}{x-6}$ at $x=5$

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Problem 7

Find the equation of the tangent to the graph of $y=\sqrt{x^{3}-15}$ at $(4,7)$

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Problem 8

Find the values of $x$ where the tangent to the graph of $y=2 x^{3}-8 x$ has a slope equal to the slope of $y=x$

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Problem 9

Find the equation of the normal to the graph of $y=\frac{3 x+5}{x-1}$ at $x=3$

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Problem 10

Find the values of $x$ where the normal to the graph of $(x-9)^{2}$ is parallel to the $y$ -axis.

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Problem 11

Find the coordinates where the tangent to the graph of $y=8-3 x-x^{2}$ is parallel to the $x$ -axis.

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Problem 12

Find the values of $a, b,$ and $c$ where the curves $y=x^{2}+a x+b$ and $y=c x$ $+x^{2}$ have a common tangent line at $(-1,0)$

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