For what point on the curve of y = 9 x2(the 2 is a squared) - 2x is the slope of a tangent line equal to 34 ?

1 Answer
Jun 1, 2018

#[2, 32]#

Explanation:

# y= 9x^2-2x#.....#[1]#, differentiating this expression wrt #x#,

#[dy/dx= 18x -2]# We are told that the slope[ gradient] is = to #34# therefore , #dy/dx=34#,......... so #34=18x-2# and thus #x=2#

When #x=2#, from .....#[1]# #y=9[2^2]-2[2]# = #32#

These values of #x and y# can now be used to find the equation of the tangent line to the curve at the point #[ 2, 32 ]#