Let f(x) = x + #sqrt(x)#?

Question

Let f(x) = x + #sqrt(x)#
. The equation for the tangent line at the point ( 9, 12 ) is y=m(x-9) +12, where m is a constant. Find the value of m.

705 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-19T18:13:38

#m = 7/6#

#$m# is the slope of the tangent line at the point where #x=9#, so #m = f'(9)#

#f'(x) = 1+1/(2sqrtx)#

#f'(9) = 1+1/(2sqrt9) = 1+1/6 = 7/6#