7A - Tangents and normal lines
■ A tangent line touches a curve exactly once at a point, \(P\). ■ A normal line is perpendicular to a tangent line at a point, \(P\).
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7A - Example 1: Finding the equation of a normal line (VCAA, 2005)
[VCAA, 2005 Exam 1 MC Question 23]
The equation of the normal to the graph of \(y=2x^4-4x^2\) at the point where \(x=2\) is A. \(y=-\frac{1}{16}\) B. \(y=-\frac{1}{16}(x-2)\) C. \(y=16\) D. \(y=16(x-2)\) E. \(y=(8x^3-12x^2)(x-2)\) |
7A - Example 1: Video solution
7A - Example 1: Practice
Question 1: ABC 7A - Example 1: Solutions
Question 1: ABC |
7A - Example 2: Finding the equation of a normal line (VCAA, 2006S)
[VCAA, 2006S Exam 2 MC Question 17]
The equation of the normal to the curve with equation \(y=2x^{\frac{3}{2}}\) at the point where \(x=4\) is A. \(y=-\frac{1}{6}x+\frac{50}{3}\) B. \(y=6x-18\) C. \(y=6x-8\) D. \(y=6x+40\) E. \(y=160x-62\) |
7A - Example 2: Video solution
7A - Example 2: Practice
Question 1: ABC 7A - Example 2: Solutions
Question 1: ABC |
7A - Example 3: Normal lines to a curve (VCAA, 2006)
[VCAA, 2006 Exam 1 Question 8]
A normal to the graph of \(y=\sqrt{x}\) has equation \(y=-4x+a\), where \(a\) is a real constant. Find the value of \(a\). |
7A - Example 3: Video solution
7A - Example 3: Practice
Question 1: ABC 7A - Example 3: Solutions
Question 1: ABC |
7A - Example 4: Tangent lines to a curve (VCAA, 2009)
[VCAA, 2009 Exam 1 Question 8]
Let \(f:R\rightarrow R, f(x)=e^x+k\), where \(k\) is a real number. The tangent to the graph of \(f\) at the point where \(x=a\) passes through the point \((0,0)\). Find the value of \(k\) in terms of \(a\). |
7A - Example 4: Video solution
7A - Example 4: Practice
Question 1: ABC 7A - Example 4: Solutions
Question 1: ABC |
7A - Example 5: Tangent lines to a curve (VCAA, 2010)
[VCAA, 2010 Exam 1 Question 10]
The line \(y=ax-1\) is a tangent to the curve \(y=x^{\frac{1}{2}}+d\) at the point \((9,c)\). Where \(a\), \(c\) and \(d\) are real constants. Find the values of \(a\), \(c\) and \(d\). |
7A - Example 5: Video solution
7A - Example 5: Practice
Question 1: ABC 7A - Example 5: Solutions
Question 1: ABC |