Application of DerivativeHard
Question
The real number k for which the equation 2x3 + 3x + k = 0 has two distinct real roots in [0, 1]
Options
A.lies between 1 and 2.
B.lies between 2 and 3.
C. lies between -1 and 0
D.does not exist
Solution
f(x) = 2x3 + 3x + k
f′(x) = 6x2 + 3 > 0
⇒ f is increasing function
⇒ f (x) = 0 has exactly one real root. (as it is an odd degree polynomial)
Create a free account to view solution
View Solution FreeMore Application of Derivative Questions
At what point the tangent to the curve √x + √y = √a is perpendicular to the x- axis-...Let f(x) = Equation of tangent line touching both branches of y = f(x) is...The inclination of the tangent w.r.t. x-axis to the curve x2 + 2y = 8x - 7 at the point x = 5 is...The curve x2 - y2 = 5 and = 1 cut each other at any common point at an angle-...If the point (1,3) serves as the point of inflection of the curve y = ax3 + bx2 then the value of ′a′ and &#...