Question

number of point of inflection on the curve f(x) =tanx-sinx , x belongs to (1, 10) is​

Answer 1

Answer:

3

in graph of tanx-sinx as you can see there are 3 points where graph change sign

Answer 2

Concept:

A point of inflection is the point on a curve when it transitions from sloping up or down to sloping up or down; it's also called concave upward or concave downward.

Given:

The function $f(x) = tanx-sinx$

Find:

The number of points of inflection.

Solution:

$f(x) = tanx-sinx\\f'(x) = sec^2x-cosx\\f''(x) = 2sec^2xtanx+sinx\\f''(x) = 0\\2sec^2xtanx+sinx=0\\2sec^2xtanx = -sinx\\2sec^3x = -1\\\\secx = (\frac{1}{2})^{\frac{1}{3} }$

$x$ as no solution.

Hence, there are no possible points to satisfy the equation.