CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
If x = t² and y = t³ + 1, then dy/dx at t = 2 is:
For parametric equations, dy/dx = (dy/dt)/(dx/dt) = 3t²/2t = 3t/2. At t = 2 this equals 3, so the slope is 3.
- A3Correct
- B6
- C12
- D4
Explanation
dy/dt = 3t² and dx/dt = 2t, so dy/dx = 3t²/2t = 3t/2. At t = 2, dy/dx = 3. Option 12 is dy/dt alone at t = 2, ignoring division by dx/dt.
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