Tangent line to a curve at a point and local linear approximation

Practice Questions

AP Calculus AB › Tangent line to a curve at a point and local linear approximation

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10 of 16

1

Give the equation of the line tangent to the graph of the equation

$f(x) = 4x+ e^{x-2}$

at the point .

2

Find the minimum value of $f(x)=\frac{1}{\sqrt{9-x^2}}$

3

Find the equation of the line tangent to $f(x)=x^{3}-3x^{2}+2x+4$ at the point .

4

Find the equation of the line tangent to $f(x)=\frac{3}{x}+x^{2}$ at .

5

Let $h(x)=\sin(x)-2x\cos(x)$ . Find the equation of the line tangent to at the point $(\pi, 2\pi)$ .

6

Find the tangent line. Given the point (1,2)

7

Give the equation of the line tangent to the graph of the equation

$f(x) =3 \sin \frac{x}{2} +2 \cos \frac{x}{3}$

at the point .

8

Find the line tangent at the point (0,1)

$y=e^{3x}$

9

Find the tangent line given the point (2,4) and the equation

10

Find the equation of the line perpendicular to the line tangent to the following function at x=1, and passing through (0, 6):

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