Question

The value of f’(x) is -1 at the point P on a continuous curve y = f(x). What is the angle which the tangent to the curve at P makes with the positive direction of x axis?

(a) π/2

(b) π/4

(c) 3π/4

(d) 3π/2

This question was posed to me at a job interview.

Asked question is from Application of Derivative topic in chapter Application of Derivatives of Mathematics – Class 12

Answer 1

The correct answer is (c) 3π/4

Explanation: Let, Φ be the angle which the tangent to the curve y = f(x) at P makes with the positive direction of the x axis.

Then,

tanΦ = [f’(x)]p = -1

= -tan(π/4)

So, it is clear that this can be written as,

= tan(π – π/4)

= tan(3π/4)

So, Φ = 3π/4

Therefore, the required angle which the tangent at P to the curve y = f(x) makes with positive direction of x axis is 3π/4.