Question

At which point does f(x) will attain local minima if f(x) = 0∫^x (t+1)(e^t – 1)(t – 2)(t + 4) dt?

(a) 0

(b) -1

(c) 1

(d) -4

I have been asked this question during a job interview.

The question is from First Order Derivative topic in section Limits and Derivatives of Mathematics – Class 11

Answer 1

Correct answer is (b) -1

The explanation: Here, f(x) = 0∫^x (t + 1)(e^t – 1)(t – 2)(t + 4) dt

So, f’(x) = (x + 1)(e^x – 1)(x – 2)(x + 4)

So, ────^+───-4|─────^–──────-1|──────^+──────0|───────^–──────2|────^+────

Clearly, x = -1 and x = 2 are points of local minima.

As, x = 2 is not present so it is -1.