Question 1
A curve has equation \( y = 3x^2 - 5x + 1 \). The equation of the normal to this curve at the point where \( x = 2 \) is
Worked answer
🔒 Start free to see full answer
Mathematical Methods · Unit 2 · Applications of differential calculus · Graphical applications of derivatives
Determine the equation of a tangent and a normal of the graph of 𝑦 = 𝑓(𝑥).
Practise this objective
AI-marked practice questions tied to QCAA mark schemes for this exact LO. Free to start.
Start free practicePractice questions for this objective
Full questions, answers and worked solutions unlock when you start a free practice session.
Question 2
Consider the function \(f(x) = x^3 - 6x^2 + 9x + 2\). (a) Determine the gradient of the tangent to the curve at the point where \(x = 2\). (b) Hence, determine the equation of the tangent at this point. (c) Determine the equation of the normal at this point.
Worked answer
🔒 Start free to see full answer
Question 3
The curve has equation $y = x^3 - 2x + 1$. A tangent is drawn to the curve at the point where $x = 1$. (a) Determine the gradient of the tangent at this point. [1] (b) Hence determine the equation of the tangent line, giving your answer in the form $y = mx + c$. [1] (c) Determine the equation of the normal line at $x = 1$, giving your answer in the form $y = mx + c$. [1]
Worked answer
🔒 Start free to see full answer