MonotonicityHard
Question
Number of solution of the equation 3tan x + x3= 2 in
is
isOptions
A.0
B.1
C.2
D.3
Solution
f(x) = 3tan x + x3 - 2, f′(x) = 3(sec2 x + x2) > 0
⇒ f (x) is increasing in ∀ x ∈ (0, π/4)
f(0) < 0 & f
> 0
⇒ f(x) = 0 has exactly one root in
f(x) = 3tan x + x3 - 2, f′(x) = 3(sec2 x + x2) > 0
⇒ f (x) is increasing in ∀ x ∈ (0, π/4)
f(0) < 0 & f > 0
⇒ f(x) = 0 has exactly one root in
⇒ f (x) is increasing in ∀ x ∈ (0, π/4)
f(0) < 0 & f
> 0⇒ f(x) = 0 has exactly one root in
f(x) = 3tan x + x3 - 2, f′(x) = 3(sec2 x + x2) > 0⇒ f (x) is increasing in ∀ x ∈ (0, π/4)
f(0) < 0 & f
> 0⇒ f(x) = 0 has exactly one root in
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