Application of DerivativeHard
Question
If f(x) = (x - 4) (x - 5) (x - 6) (x - 7) then,
Options
A.f′(x) = 0 has four roots.
B.three roots of f′(x) = 0 lie in (4, 5) ∪ (5, 6) ∪ (6, 7)
C.the equation f′(x) = 0 has only one real root.
D.three roots of f′(x) = 0 lie in (3, 4) ∪ (4, 5) ∪ (5, 6).
Solution
f(4) = f(5) = f(6) = f(7) = 0
By Rolle′s theorem on interval
[4, 5], [5, 6], [6, 7] we have
f′(x) = 0 for at least once in each intervals (4, 5), (5, 6), (6, 7).
By Rolle′s theorem on interval
[4, 5], [5, 6], [6, 7] we have
f′(x) = 0 for at least once in each intervals (4, 5), (5, 6), (6, 7).
Create a free account to view solution
View Solution FreeMore Application of Derivative Questions
The value of c for the function f(x) = log sin x in the interval is-...If tangent at a point of the curve y = f(x) is perpendicular to 2x - 3y = 5, then at that point equal -...The equation of normal to the curve = 1 at the point (a sec θ, b tan θ) is-...The angle of intersection between the curve y2 = 16 x and 2x2 + y2 = 4 is-...The slope of the tangents to the curve y = (x + 1) (x- 3) at the points where it crosses x- axis are-...