Aptitude | GATE CS 1998 | Question 65

a. Find the points of local maxima and minima, if any, of the following function defined in 0≤ x ≤ 6.

  x3-6x+9x-15

b. Integrate

Answer:

Explanation: (a)

f(x)= x^3-6x^2+9x-15
f'(x) = 3x^2-12x+9
f''(x) = 6x-12

For finding critical point

Now f'(x) =0

3x^2-12x+9=0

After solving, we get

x=3 or x=1

Now, f”(x)= 6x-12. Put x=3 we get positive value at x=3
Hence, local minima =3

f”(x)= 6x-12. put x=1 we get negative value at x=1

Hence, local maxima =1

(b)

f(x)= ∫x cosx dx where upper limit π and lower limit is -π.

Here x is an odd function and cos x is an even function so x cos x is an odd function.

As we know that if g(x) is odd function then ∫g(x) dx = 0 upper limit a and lower limit is -a.

Hence, f(x)= ∫x cos x dx where upper limit π and the lower limit is -π having value 0.

Quiz of this Question