Find the best solutions to your problems with the help of IDNLearn.com's experts. Our experts provide timely and accurate responses to help you navigate any topic or issue with confidence.
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.