Question Detail

MTH 102 Differentiation Objective Question
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Question

Find the equation of the normal to \( y = x^3 - 4x^2 + 1 \) at \( x=2 \).
Options
A \( 4y = x - 30 \)
Correct Answer
B \( y = -4x + 1 \)
C \( y = 4x - 15 \)
D \( 4y = x + 30 \)
Correct Answer

Option A is the correct answer.

Detailed Explanation

( y' = 3x^2 - 8x ). At ( x=2, y' = 12 - 16 = -4 ). Normal slope ( m = 1/4 ). Point is ( (2, -7) ). Line: ( y+7 = 1/4(x-2) \implies 4y+28 = x-2 \implies 4y = x-30 ).

Hint

Normal slope is the negative reciprocal of the tangent slope.

Question Info

Course: MTH 102
Topic: Differentiation
Type: Objective
Difficulty: Not specified
Question 174 of 930
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