28. At which of the five points on the graph in the figure above is \( \dfrac{dy}{dx} > 0 \) and \( \dfrac{d^2y}{dx^2} > 0 \)?






Answer is: option2

B

Solution:

dy/dx > 0

This means the graph is increasing at that point — it's going upward as you move right.

dy/dx > 0

This means the graph is concave up at that point — the slope is increasing, and the graph is curving upwards like a smile.

Point A:
Decreasing (slope < 0), and concave down — ❌

Point B:
The graph has just started increasing — so
dy/dx > 0
✅ Concave up — the curve is opening upward.
✅ This is a match.

Point C:
Still increasing (slope > 0), but
❌ Concave down — the curve is bending downward.

Point D:
Decreasing (slope < 0) and concave down — ❌

Final Answer: (B) B
At Point B, the curve is increasing and concave up, satisfying both conditions:
dy/dx > 0 and d²y/dx² > 0.

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