If f (x) is a polynomial of degree 5 with real coefficients such that has 8 real roots then f (x) = 0 has:
5 real roots
Given that has 8 real roots.
Since f (x) is a polynomial of degree 5, f (x) cannot have even number of real roots.
⇒ f (x) has all the five roots real in which four positive and one root is negative.
If f (x) = loge x and g(x) = x2 and c Ïµ (4, 5), then is equal to:
In [0, 1] lagrange’s mean value theorem is not applicable to
Let f (x) satisfy the requirement of lagrange’s mean value theorem in [0, 2]. If f (0) and
Let f : [2, 7] and [0, ∞) be a continuous and differentiable function.
Then the value of (f (7) – f (2)) is (where c Ïµ (2, 7))
The equation sin x + x cos x = 0 has at least one root in the interval
Let f (x) = ax5 + bx4 + cx3 + dx2 + ex, where a, b, c, d, e Ïµ R and f (x) = 0 has a positive root α, then
Between any two real roots of the equation ex sin x – 1 = 0, the equation excos x + 1 = 0 has
f (x) is a polynomial of degree 4 with real coefficients such that f (x) = 0 is satisfied by x = 1, 2, 3 only, then f’(1). f’(2). f’(3) is equal to:
If the function f (x) = | x2 + a | x | +b| has exactly three points of non-differentiability, then which of the following can be true?