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Engineering Mathematics
Calculus
GATE 2021
Easy

Let f(x) = x² - 2x + 2 be a continuous function defined on x ∈ [1,3]. The point x at which the tangent of f(x) becomes parallel to the straight line joining f(1) and f(3) is

  • A0
  • B1
  • 2
  • D3

Explanation

f(1)=1, f(3)=5, so the secant slope is (5-1)/(3-1)=2. f'(x)=2x-2. Setting 2x-2=2 gives x=2 (guaranteed to exist in (1,3) by the Mean Value Theorem).

Source: GATE ME 2021 Session 1 (ME-1) (2021)

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