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Sagot :
Answer:
k=16
Step-by-step explanation:
So the tangent line is
[tex]4x + k[/tex]
and it tangent to function
[tex] {x}^{2} + 8x + 20[/tex]
Since the slope of the tangent line is 4, this means the derivative of f(x) is 4 but first let find the derivative of
[tex] {x}^{2} + 8x + 20[/tex]
Use the Sum Rule,
[tex] \frac{d}{dx} {x}^{2} + \frac{d}{dx} 8x + \frac{d}{dx} 20[/tex]
Use the Power Rule and we get
[tex]2x + 8[/tex]
Set this equal to 4
[tex]2x + 8 = 4[/tex]
[tex]2x = - 4[/tex]
[tex]x = - 2[/tex]
So at x=-2, the slope of the tangent line is 4.
Plug -2 in the orginal function, and we get
[tex] { - 2}^{2} + 8( - 2) + 20 = 8[/tex]
So the point must pass through -2,8 with a slope of 4.
[tex]y - 8 = 4(x + 2)[/tex]
[tex]y - 8 = 4x + 8[/tex]
[tex]y = 4x + 16[/tex]
So the value of k is 16.
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