alleryLocal maximum of f at x = c (if f'(c) = 0):
Af''(c) > 0
Bf''(c) < 0 (concave down)
Cf''(c) = 0
Df'''(c) = 0
Answer & Solution
Correct answer: B. f''(c) < 0 (concave down)
**Second derivative test:** if f'(c) = 0 and f''(c) < 0, then c is a local max.
If f''(c) > 0, c is local min. If f''(c) = 0, test inconclusive.
Keep practising Unit 4-5: Applications of Derivatives & Curve Sketching
Browse all Unit 4-5: Applications of Derivatives & Curve Sketching questions for AP Calculus AB, or explore more Mathematics topics.
Related questions
If the tangent to the curve $y = e^{2x}$ at point $(a, e^{2a})$ passes through origin, theIf $f(x) = x^x$ for $x > 0$, then $f$ has a minimum at $x = $:The function $f(x) = \dfrac{x}{1 + x^2}$ attains its maximum value on $[0, \infty)$ at:Find the **shortest distance** from origin to the curve $xy = 4$ (in the first quadrant):A rectangle is inscribed in a semicircle of radius $R$ with base on the diameter. The **maThe function $f(x) = x^3 - 3x + 1$ has critical points at:$f(x) = 2x^3 - 3x^2 - 12x + 5$. The **local maximum value** occurs at:Find the approximate value of $ qrt{25.5}$ using differentials (given $ qrt{25} = 5$):