Question
Question: f(x) = e<sup>x</sup>. cos x, x ∈ [0, 2π]. The slope of tangent of the function is minimum for...
f(x) = ex. cos x, x ∈ [0, 2π]. The slope of tangent of the function is minimum for
A
x = π
B
x = π/4
C
x = 3π/4
D
x = 3π/2
Answer
x = π
Explanation
Solution
f(x) = ex cosx
⇒ f '(x) = ex(cosx − sinx)
⇒ f "(x) = ex(−2 sinx)
Sign scheme of f"(x) is,
That mean x = π is the point of minima of f '(x).