Question

Determine the value of k if g(x) =4x + k is a tangent to f(x) =-x^2 +8x +20

Answer 1

Given : g(x)= 4x+k is a tangent to f(x)= -x² +8x +20

To Find : Value of k

Solution:

g(x) = 4x  + k   is a tangent to f(x)= -x² +8x +20

f(x)= -x² +8x +20

=> f'(x)  =  -2x  + 8

slope of tangent = -2x + 8  at ( x , y)

g(x) = 4x  + k   hence slope = 4

 -2x  + 8 = 4

=> -2x = - 4

=> x = 2

f(x)= -x² +8x +20

x = 2

=> y = -2² + 8(2) + 20  =  32

(2 , 32)

Hence (2 , 32) lies on g(x)= 4x+k

=> 32 = 4(2) + k

=> k = 24

Value of k = 24

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