Application of DerivativeHard
Question
If f(x) = a ln |x| + bx2 + x has its extremum values at x = - 1 and x = 2, then
Options
A.a = 2, b = - 1
B.a = 2, b = - 1/2
C.a = - 2, b = 1/2
D.none of these
Solution
f′(x) = a/x + 2bx + 1
f¢(- 1) = 0
- a - 2b + 1 = 0
a + 2b = 1
f′(2) = 0
a/2 + 4b + 1 = 0 ⇒ a + 8b + 2 = 0
- 6b = 3 ⇒ b =
, a = 2
f¢(- 1) = 0
- a - 2b + 1 = 0
a + 2b = 1
f′(2) = 0
a/2 + 4b + 1 = 0 ⇒ a + 8b + 2 = 0
- 6b = 3 ⇒ b =
, a = 2 Create a free account to view solution
View Solution FreeMore Application of Derivative Questions
The radius of an air bubble is increasing at the rate of 0.5 cm/sec. The rate by which the volume of the bubble is incre...The tangent to the curve x = a(θ − sinθ ), y = a(1 + cosθ) at the points = (2k + 1)π, k∈...Equation of common tangent(s) of x2 - y2 = 12 and xy = 8 is (are) -...If 27a + 9b + 3c + d = 0, then the equation 4ax3 + 3bx2 + 2cx + d = 0, has atleast one real root lying between -...At the point P(a, an) on the graph of y = xn(n ∈ N) in the first quadrant a normal is drawn. The normal intersects...