Rajasthan Board Class 12 (RBSE) Application of Derivatives — practice questions
13 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice Rajasthan Board Class 12 (RBSE) Application of Derivatives in the app →A function $f$ is increasing on an interval if, on that interval:The slope of the tangent to $y = x^2$ at $x = 3$ is:By the second derivative test, a critical point $c$ of $f$ with $f''(c) > 0$ is a:At a local maximum of a differentiable function $f$ on its domain:A function f(x) is INCREASING on an interval if for all x in the interval:The tangent to y = x² at the point (1, 1) has slope:Rolle's theorem requires that on [a, b], in addition to continuity + differentiability:At a critical point c where f'(c) = 0, if f''(c) > 0, then c is a:To find the dimensions of a rectangle with maximum area + perimeter 20, set up:The critical points of f(x) = x³ − 3x + 1 are found by solving f'(x) = 0:A balloon is inflated so its volume V = (4/3)πr³ increases at 8π cm³/s. When r = 2 cm, the rate of change of rFor a particle moving along x(t) = t³ − 3t² + 5, the velocity at t = 2 is:At the optimal production level (maximum profit), in marginal analysis: