Question

examine function f(x)=x^3+3x^2 for maxima and minima.​

Answer 1

Answer:

Our function

f(x) = x^3 + 3x^2

To differentiate this function on both sides with respect to x

f'(x) = 3x^2 + 6x = 3x ( x + 2)

Clearly f'(x) = 0 at x = 0 and x= -2

Now,

f''(x) = 6x + 6

f''(0) = 6

since f"(0)>0 implies the function f(x) has minimum at x = 0

Now,

f"(-2) = -6 < 0 implies the function f(x) has maximum at x= -2

Hope this helps you !