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? support@testustad.com
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.
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?