Respuesta :
The value of k in the given functions is; 24
What is the value of the function to the tangent?
We are given the functions;
g(x) = 4x + k as a tangent to f(x) = -x² +8x +20
For f(x) = -x² +8x +20
=> f'(x) = -2x + 8
Thus, slope of tangent at ( x , y) = -2x + 8
For g(x) = 4x + k
g'(x) = 4.
Thus, slope is 4
Therefore;
-2x + 8 = 4
-2x = -4
x = 2
Putting 2 for x in f(x) gives;
f(2) = -2² + 8(2) + 20
f(2) = 32
Thus, it is at (2 , 32)
Thus, (2 , 32) lies on g(x) = 4x + k
4(2) + k = 32
k = 32 - 8
k = 24
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