Application & Interpretations
Calculus
Contents: Click to skip to subtopic
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.1: Limits, slopes of curves
5.2: Increasing & decreasing regions
5.3: Derivatives of polynomials
Problems:
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If f(x) = 4x², find f'(x):
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If g(x) = 5x³ - 2x, find g'(x):
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If f(x) = x⁻ ² + 7, find f'(x):
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If y = x + 12 - 2x, find dy/dx:
Answer
8x
Answer
15x² - 2
Answer
-2x⁻³
Answer
-1
5.4: Equations of tangents and normals
Exercises
Solutions
5.5: Introduction to integration
Problems:
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Find ∫2xdx:
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Find ∫(4t³-2)dt:
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Find ∫9x²dx:
Answer
x²
Answer
t⁴ - 2t
Answer
3x³
5.6: Turning Points
5.7: Optimisation
5.8: Trapezoidal Rule
