top of page
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
AI5.1
5.1: Limits, slopes of curves

AI5.2
5.2: Increasing & decreasing regions

AI5.3
5.3: Derivatives of polynomials

Problems:
-
If f(x) = 4x², find f'(x):
-
If g(x) = 5x³ - 2x, find g'(x):
-
If f(x) = x⁻ ² + 7, find f'(x):
-
If y = x + 12 - 2x, find dy/dx:
Answer
8x
Answer
15x² - 2
Answer
-2x⁻³
Answer
-1
AI5.4
5.4: Equations of tangents and normals

Exercises

Solutions

AI5.5
5.5: Introduction to integration

Problems:
-
Find ∫2xdx:
-
Find ∫(4t³-2)dt:
-
Find ∫9x²dx:
Answer
x²
Answer
t⁴ - 2t
Answer
3x³

AI5.6
5.6: Turning Points

AI5.7
5.7: Optimisation

AI5.8
5.8: Trapezoidal Rule

bottom of page