Question

if normal to the curve y=f(x) at the point (3,4) makes an angle 3pie/2 with the positive x axis then f ' (3) is equal to?

Answer 1

$\mathrm{We}\mathrm{know},\frac{3\mathrm{\pi }}{2}=270°,\mathrm{i},\mathrm{e}\mathrm{angle}\mathrm{is}90°\mathrm{to}\mathrm{the}\mathrm{x}-\mathrm{axis}\mathrm{in}\mathrm{the}\mathrm{downward}\mathrm{direction}.$
The normal is parallel to y-axis,so tangent to the curve at that point.i,e(3,4) is parallel to the x-axis.
So, f ' (3)=0 as slope =0