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Class XII Maths Applications of Derivatives 2

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Question 1

If each a_i > 0, then the shortest distance between the point (0, –3) and the curve y = 1 + a₁x² + a₂x⁴ + ……+ a_nx²ⁿ is

Question 2

The function f(x) =

has a local minimum at

Question 3

Suppose the cubic x³ – px + q has three distinct real roots where p > 0 and q > 0. Then which one of the following holds?

Question 4

If the function f (x) = 2x³ − 9ax² + 12a² x + 1, where a > 0, attains its maximum and minimum at p and q respectively such that p² = q, then a equals

Question 5

The real number k for which the equation, 2x³ + 3x + k = 0 has two distinct real roots in [0, 1]

Question 6

If x is real, the maximum value of

Question 7

The positive real number x, when added to its inverse, gives the minimum value of the sum at x equal to

Question 8

Let f: R → R be defined by

If f has a local minimum at x = –1, then a possible value of k is

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Apr 20JEE & BITSAT