Question

find k such that the line is tangent to the graph of the function fuction= f(x)=x^2-kx line y=4x-9

Answer 1

find the 1st derivative..

Answer 2

i did

Answer 3

ok... the gradient/slope of the given line

y = 4x - 9 is..?

Answer 4

4

Answer 5

ok what do i do

Answer 6

so you need to set the 1st derivative equal to 4 and solve for k

Answer 7

i solved for k k=2x-4

Answer 8

ok... so you have

\[x^2 - (2x - 4)x\]

you need to now find the point of intersection so equate the parabola and line

x^2 - (2x - 4)x = 4x - 9

after simplifying

-x^2 = -9

x^2 = 9

so x = 3

(3, 3) is the point of intersection.

Answer 9

thanks!

Answer 10

so m = 4 when x = 3

so using the 1st derivative

4 = 2(3) - k

k = 2

hope it makes sense... it was a bit more difficult than I thought...