Number and Algebra
Functions
Geometry & Trigonometry
Statistics & Probability
Calculus
Consider the curve defined by y=ln(x)y = \ln(x)y=ln(x).
Find the equation of the normal to the curve at x=4x=4x=4.
Determine the equation of the normal to the curve y=arctan(x)y=\arctan(x)y=arctan(x) at x=1x=1x=1.
Calculate the equation of the normal to the curve y=e2x+xy = e^{2x} + xy=e2x+x at the point where the tangent has slope 5.
Consider the curve defined by the equation y=sinx+xy = \sin x + xy=sinx+x for 0≤x≤π0 \le x \le \pi0≤x≤π.
Find the equation of the normal to the curve at the point where the tangent has a gradient of 1.
Find the equation of the normal to the curve x3+y3=6xyx^3+y^3=6xyx3+y3=6xy at the point (3,3)(3,3)(3,3).
Find the equation of the normal to the curve y=xx−1y=\tfrac{x}{x-1}y=x−1x at x=2x=2x=2.
Find the equations of the normals to the curve y=x3−3x+2y = x^3 - 3x + 2y=x3−3x+2 at the points where the tangent has slope 6.
Find the equation of the normal to the curve defined by x2+xy+y2=7x^2+xy+y^2=7x2+xy+y2=7 at the point (1,2)(1,2)(1,2).
Determine the equation of the normal to the curve y=1xy = \frac{1}{x}y=x1 at the point where x=−1x = -1x=−1.
Calculate the equation of the normal to the curve y2=4x+8yy^2=4x+8yy2=4x+8y at the point (0,0)(0,0)(0,0).
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Question Type 1: Finding the tangent and normal to a polynomial at a specific value of x
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Question Type 3: Finding the tangent and normal to more complex functions using the GDC at different points
