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VICMath MethodsQuick questions
Unit 1
Quick questions on Rates of change and the derivative: VCE Math Methods Unit 1 Year 11
9short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What is worked examples?Show answer
$f(x) = x^4$: $f'(x) = 4 x^3$.
What is worked example?Show answer
$y = x^2 - 4 x + 3$ at $x = 1$. $f(1) = 1 - 4 + 3 = 0$.
What is tangent?Show answer
The line touching the curve at one point with the same gradient as the curve.
What is normal?Show answer
Perpendicular to the tangent at the same point.
What is forgetting the limit definition?Show answer
Average rate is a finite difference; instantaneous rate is the limit. They are different in general but related.
What is power rule applied to non-power functions?Show answer
The power rule applies to $x^n$. It does not directly apply to $e^x$, $\sin x$, or $\ln x$ (those are introduced in Unit 3).
What is tangent gradient confused with the function value?Show answer
$f(a)$ is the function's value at $a$. $f'(a)$ is the gradient at $a$. Different objects.
What is forgetting to factor before finding stationary points?Show answer
$f'(x) = 0$ requires solving for $x$; factor first.
What is wrong normal gradient?Show answer
Normal gradient is $-1 / m$ where $m$ is the tangent gradient. Sign and reciprocal both matter.