Find the points on the curve `y=3x^2-9x+8` at which the tangents are equally inclined with the axes.

Answer

Point is `(frac{5}{3}, frac{4}{3})`

Explanation

Given the curve is `y=3 x^{2}-9 x+8`.


Now, `\frac{d y}{d x}=6 x-9 \ldots .(1)`


Slope of the tangent at `(x, y)` is `\frac{d y}{d x}`.


If the tangent at `(x, y)` is equally inclined to the axis then the slope of the tangent is `1`

Then from eq (1);

$$ 6 x-9=1 $$
...