Curve C has equation
y=x^3+x^2-5x+3
there are two points on C where the gradient of the tangent to C is equal to 3.
Find the x coordinates of these two points.
Can you pls explain it to me clealry! Thank u very much
Take the first derivative and set f'(x) to 3.
$\displaystyle f'(x) = 3x^2 - 5 = 3 \rightarrow f'(x) = 3x^2 - 8 = 0$
solve using the difference of two squares:
$\displaystyle (\sqrt3 - 2\sqrt2)(\sqrt3 + 2\sqrt2) = 0$
so $\displaystyle x = \frac{2\sqrt2}{\sqrt3}$ or $\displaystyle x = -\frac{2\sqrt2}{\sqrt3}$