Question

At an extreme point of a function $f\left(x\right)$, the tangent to the curve is

• A. Parallel to the $x$-axis
• B. Perpendicular to the $x$-axis
• C. Inclined at an angle ${45}^{\circ }$ to the $x$-axis
• D. Inclined at an angle ${60}^{\circ }$ to the $x$-axis

Answer 1

The correct option is A Parallel to the $x$-axis

At an extreme point of a function $f\left(x\right)$, slope is always zero.
Thus, at an extreme point of a function $f\left(x\right)$, the tangent to the curve is parallel to the $x$-axis.