Home › Bihar Board Class 12 (Commerce) › Mathematics › Application of Derivatives › Find the smallest a for which f(x) = x² + ax + 1…
Find the smallest a for which f(x) = x² + ax + 1 is increasing on [1, ∞).
A−2
B−4
C0
D2
Answer & Solution
Correct answer: A. −2
f'(x) = 2x + a must be at least 0 for all x ≥ 1, and its least value 2 + a is zero when a = −2.
Related questions
How fast does the area of a square change per unit change in its side when the side is 4?A differentiable function is increasing on an interval if which condition holds there?If f' changes from positive to negative as x increases through c, what does f have at c?Water enters a cylindrical tank of radius 2 m at 8 pi m^3/min. How fast does the level risA ripple's radius grows at 2 cm/s. How fast does its circumference grow?A spherical balloon gains volume at 8 pi cm^3/s. How fast does r grow when r = 2 cm?A sphere's radius is measured with a 3 percent error. What is the approximate percent erroIf y = x^2, what is dy when x = 3 and dx = 0.02?