GATE Chemical 2014 | GA | Question: 4

Question

If $y=5x^{2}+3,$ then the tangent at $x=0,y=3$

• A. passes through $x=0,y=0$
• B. has a slope of $+1$
• C. is parallel to the $x$-axis
• D. has a slope of $-1$

Answer 1

Option C is Correct.

More about Tangent

• Slope = 0 → Line is parallel to x-axis

• Slope > 0 → Line goes upward (left to right)

• Slope < 0 → Line goes downward (left to right)

• Slope = +1 → Line rises at 45°

• Slope = −1 → Line falls at 45°

So in general:

 If slope ≠ 0, the tangent is slanted, not horizontal.