1 of 8 0-day streak

Apply tangent and normal geometry to a polynomial curve

Question 1 of 8

No calculator

Distinguish the curve point from the tangent gradient

f(x)=x^{2}-4x+2,\quad x\in\mathbb R

Find the tangent at the stated input

x=2

(a)3 marks

Enter each contact input, its curve height and its tangent gradient. For multiple contacts, use increasing input order

\(x_1\) \(y_1\) \(f'(x_1)\)

(b)3 marks

Enter the coefficients of each required line in the printed canonical form. Use integers with no common factor, and choose A positive; if A is zero, choose B positive. The constant is on the left

A_i x+B_i y+C_i=0

\(A_1\) \(B_1\) \(C_1\)

Which method is valid for an arbitrary polynomial at a specified contact?

Use the original function value as the tangent gradient

A tangent must pass through the origin

Use the original function for the point height and the derivative for the tangent gradient

Use the derivative value as the point height