Question
Asked Oct 27, 2019
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Finding derivative.

1
Suppose f(x)
2а + 6
Find an equation for the tangent line to the graph of y
f(x) when x
5.
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1 Suppose f(x) 2а + 6 Find an equation for the tangent line to the graph of y f(x) when x 5.

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Expert Answer

Step 1

Given,

1
f (x)
2.х+6
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1 f (x) 2.х+6

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Step 2

Now, differentiating on both sides, we get

1
2x+6
f'(x)
dx
d(2x+6)-1
dx
x d(2x+6)
-(2x 6)-1-1
X
dx
-(2x 6)2 x (2 0)
2
(2.x+6)2
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1 2x+6 f'(x) dx d(2x+6)-1 dx x d(2x+6) -(2x 6)-1-1 X dx -(2x 6)2 x (2 0) 2 (2.x+6)2

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Step 3

Slope of the tangent line is given ...

df(x)
dx x-5
So, slope of the tangent at x = 5 is
2
(2x5+6)2
256
1
128
1
And when x 5 then f (5)
2(5)+6
16
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df(x) dx x-5 So, slope of the tangent at x = 5 is 2 (2x5+6)2 256 1 128 1 And when x 5 then f (5) 2(5)+6 16

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Math

Calculus

Derivative

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