The point of inflection of the function The point of inflection of the function y = ∫(t2 - 3t + 2)dt x ∈[0,x] is :

Question

The point of inflection of the function 

y = ∫(t² - 3t + 2)dt   x ∈[0,x] is :

(A)  (1/2, 3/2)

(B)  (3/2, 3/4)

(C)  (-3/2, -3/4)

(D)  (-1/2, - 3/2)

Answer 1

Correct option  (B)  (3/2, 3/4)

Explanation:

Given y = ∫(t² - 3t + 2)dt   x ∈[0,x } Differentiating w.r.to x, we have dy/dx = x²- 3x + 2 & d²y/dx² = 2x -3.

At the point of inflection d²y/dx² = 0 & second derivative changes sign while passing through the point of inflection.

Clearly P(3/2, 3/4).