For the curve y = x³ - 2x + 1, what is the equation of the normal at x = 1?
Correct answer: D. y - 2 = -(1/1)(x - 1)
- A. y - 1 = (1/1)(x - 1)
- B. y - 1 = -(1/1)(x - 1)
- C. y - 2 = (1/1)(x - 1)
- D. y - 2 = -(1/1)(x - 1)
Explanation
At x = 1, the curve has y = 0, not y = 1 or 2. Since dy/dx = 3x² - 2, the tangent slope is 1 and the normal slope is -1, so y = -x + 1, written as y - 0 = -(x - 1). The listed option d contains y - 2 and is therefore incorrect as written.
Report an error
The more specific you are, the faster it gets fixed. A source beats an opinion.
Prefer email? [email protected]
About Differentiation and Optimisation
Differentiation covers gradients, standard derivative rules, the product and quotient rules, the chain rule, stationary points and rates of change. Optimisation uses first and second derivatives to classify maxima and minima, while applications include tangent and normal lines, marginal quantities and related rates.
Practise Differentiation and Optimisation
30 free Differentiation and Optimisation MCQs from Quantitative Methods, each with the correct answer and an explanation. Unlimited attempts, no account needed.
Discussion
Stuck on an option, or know a faster way to get there? Ask or explain it here.
No comments yet. Be the first to explain this one.
Exams that ask Quantitative Methods questions like this
Quantitative Methods is on this paper prepared for on TestUstad, and all of them draw the same bank, so this question is worth knowing for it.
More Differentiation and Optimisation questions
Two positive numbers have sum 20. What is the maximum possible value of their product?
Let f be differentiable and invertible, with f(3) = 7 and f'(3) = 5. What is (f⁻¹)'(7)?
The marginal cost of producing q units is MC(q) = 2q + 10, and the marginal revenue is MR(q) = 50 - 2q. At what positive output is profit stationary?
A spherical balloon is inflated so that its radius increases at 2 cm per second. At the instant its radius is 3 cm, how fast is its volume increasing?
What is the absolute minimum value of f(x) = x² - 4x + 7 on the interval [0, 5]?
Using Lagrange multipliers, which condition identifies a constrained stationary point of f(x, y) subject to g(x, y) = 0?