Question

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 ?

Answer 1

`[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 ]`