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Tutor AI · Calculus · Continuity
Mathematics › Calculus › Continuity & Differentiability
Hey student. Ask me about limits, derivatives, or continuity for Class 12 boards.
A
What's the difference between continuous and differentiable?
Differentiability is the stronger condition.
If f is differentiable at x = a, then f is continuous at x = a.
  • Derivative = slope at one exact point.
  • If the graph breaks, no single slope exists.
Question 4 of 8
5 pts Written Response
Differentiate f(x) = x³ + 2x² − 5x, then evaluate f′(2).
Fractions a/b ½
Powers & Roots x² xⁿ √
Operations ± × ≤
1 Step 1 — Differentiate: f′(x) = 3x² + 4x − 5
2 Step 2 — Substitute x = 2: f′(2) = 3(4) + 4(2) − 5 = 12 + 8 − 5 = 20
Previous Next
Your Score 42/50 84%
Q4 · 5 pts
~ Partial 4 / 5 pts
Differentiate f(x) = x³ + 2x² − 5x, then evaluate f′(2).
Your Answer
Step 1 — Differentiate: f′(x) = 3x² + 4x − 5 2/2
Step 2 — Substitute x = 2: f′(2) = 3(4) + 4(2) − 5 = 12 + 8 − 5 = 20 2/3
Why you lost marks
Step 1 is fully correct. In Step 2 the arithmetic is off — 12 + 8 − 5 = 15, not 20.
To improve
Write out each term before summing so small arithmetic slips don't cost marks.
June 2026
● Physics Exam 14d ● Maths Test 6d
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Physics 45%
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Edvion AI
Online
Me
Can you explain Newton's Third Law?
E
For every action, there is an equal and opposite reaction. When you push a wall, the wall pushes you back with the same force!
Me
Give me an example with a rocket
E
A rocket expels hot gas downward (action) — so the gas pushes the rocket upward (reaction). That's why rockets work even in the vacuum of space!
E
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Science · Class 10 · Chapter 7
9 / 25
Which products are formed during anaerobic respiration in yeast?
✓
CO₂ and ethanol
✗
CO₂ and lactic acid
C
O₂ and glucose
D
ATP and water
💡 Explanation Yeast undergoes anaerobic respiration (fermentation), breaking down glucose into ethanol and CO₂ — unlike muscle cells which produce lactic acid.
+4 marks 🔥 7 streak
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Chapter Progress
12 / 79 complete
Mathematics
Physics
Chemistry
English
Biology
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Relations and Functions
100%
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100%
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Continuity & Differentiability
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AI
AI suggests: Focus on Matrices next — you're 45% through. Two more sessions will clear it before your exam on Jul 3.
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+340 XP
12
Exams taken
82%
Avg. score
🔥 7
Day streak
Exam results
Mathematics
92%
Physics
78%
Chemistry
61%
AI
Tutor chats: 23 sessions this week — most doubts were in Chemistry. A revision session is on your organiser.
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Class 12 · Physics · Ch 3
A parallel plate capacitor has plate area A and separation d. Find the energy stored when charged to voltage V.
  1. ① Express capacitance C in terms of A and d
  2. ② Write the energy formula using C and V
  3. ③ Substitute and simplify
Edvion AI · Step-by-step
1
C = ε₀A/d — capacitance from plate geometry
2
Energy U = ½CV² — standard capacitor formula
3
Substituting: U = ε₀AV²/2d
Current Electricity · NCERT 12
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