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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
Correct answer is option 'C'. Can you explain this answer?
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The value of f’(x) is -1 at the point P on a continuous curve y ...
It is not clear what "f" refers to in this context. Can you please provide more information or clarify your question?
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The value of f’(x) is -1 at the point P on a continuous curve y ...
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.
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