Question

find the point on the cover y=x²-4x+5 where tangent to the curve is parallel to x -axis​

Answer 1

$y = x {}^{2} - 4x + 5 \\ \\ \frac{dy}{dx} = 2x - 4 \\ \\ since \: it \: is \: parallel \: to \: x \: axis \: \\ therefore \: \tan( \alpha ) = 0 = \frac{dy}{dx} \\ now \: \: 2x - 4 = 0 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \red{x = 2} \\ \\ now \: y = x {}^{2} - 4x + 5 \\ \: \: \: \: \: y = 4 - 8 + 5 \\ \: \: \: \bold \green{y = 1} \\ \\ therefore \: \boxed {p(2 \: \bold \red{and}1)} \: \bold \green {ans}$