Find k such that the line is tangent to the graph of the function. Function Line f(x) = k − x2 y = −8x + 3 k =

Answer 1

Need to have the slope of f(x) and y be equal at a point.

f'(x) = -2x

y' = -8

-2x = -8

x = 4

To find k, set x = 4 and equate both equations

-8(4) + 2k = k - (4)²

-32 + 2k = k -64

2k = 32

k = 16

If you plot both y = -8x+32 and f(x) = 16-x² you will see that the line is tangent to the function at (4,0).