Question

Explain the concept of increasing and decreasing functions using geomatrical significance of dy/dx illustrate with proper example.​

Answer 1

please thanks it make me as brilliant

Answer 2

Answer:

Increasing function

• if f(x) is an increasing function on(a, b), and X is a random point in space (a, b). Every point on the curve y=f(x) forms an acute angle 0 with the x-axis in the positive direction.

       As a result,

                      tan θ > 0 ,

                      $\frac{dx}{dy} > 0$   (or)   f(x) >  0,

Decreasing function

• If f(x) is a decreasing function on(a, b), and X is an arbitrary point in the space (a, b). At every point on the curve y=f(x), the tangent produces an obtuse angle of 0 with the positive axis direction.

      As a result,

                   tan θ  < 0

                    $\frac{dx}{dy} < 0 ,$   (or)   f(x) <o