Question

If m is the number of solution of the equation 3tanx + x³ = 2, in ( 0, π/4) and n is the number of inflection points of f(x) = 3x⁴ – 4x³, then the value of (m + n + 2) is...

Answer 1

Clearly, the number of solutions of

3tanx + x³ = 2, in (0, π/4) is 1.

Thus m = 1

Also, f(x) = 3x⁴ – 4x²

⇒ f'(x) = 12x³ – 12x²

⇒  f ≤(x) = 36x² – 24x = 12x(3x – 2)

Now, f ≤ (x) = 0 gives x = 0, 2/3

So, the number of points of inflection is 2

Thus, n = 2

Hence, the value of (m + n + 2) is 5.