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PLEASE HELP Find the slope and equation of the tangent to each of the following curves at the given point:

PLEASE HELP Find the slope and equation of the tangent to each of the following curves-example-1
User KostasC
by
8.4k points

1 Answer

14 votes

Answer:

Explanation:

To find the slope of the tangent at a point we will find the derivative of equation at that point.

a). y = x² - 10x


(dy)/(dx)=(d)/(dx)(x^(2) -10x)

y' = 2x - 10

At (x = 2),

y' = 2(2) - 10

y' = 4 - 10

y' = -6

From the given equation,

y = 2² - 10

y = -6

Therefore, y-coordinate of the point is y = -6

Equation of the tangent at (2, -6) having slope = -6

y - 2 = -6(x - 2)

y - 2 = -6x + 12

y = -6x + 14

b). y =
x^(2)+(2)/(x)

At x =
(1)/(2)

y =
((1)/(2))^2+(2)/((1)/(2))

y =
(1)/(4)+4

y =
(17)/(4)

Now we have to find the equation of a tangent at
((1)/(2),(17)/(4))

y' = 2x -
(2)/(x^(2) )

At x =
(1)/(2)

y' =
2((1)/(2))-(2)/(((1)/(2))^2)

y' = 1 - 8

y' = -7

Therefore, equation of the tangent at
((1)/(2),(17)/(4)) will be,


y-(17)/(4)=-7(x-(1)/(2))

y = -7x +
(7)/(2)+(17)/(4)

y = -7x +
(31)/(4)

User Jamie Edwards
by
8.0k points

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