# Find the points a

It is given that function is f (x) = (x – 2)4 (x + 1)3

f’(x) = 4(x - 2)3 (x + 1)3 + 3(x + 1)2(x - 2)4

=(x - 2)3(x + 1)2[4(x + 1) + 3 (x - 2)]

=(x - 2)3(x + 1)2(7x - 2)

Now, f’(x) =0

x = - 1 and x = or x = 2

Now, for values of x close to and to the left of

f’(x) > 0.

Also, for values of x close to and to the right of , f’(x) < 0.

Then, x = is the point of local maxima.

Now, for values of x close to 2 and to the left of 2, f’(x) < 0.

Also, for values of x close to 2 and to the right of 2. f’(x) > 0.

Then, x = 2 is the point of local minima.

Now, as the value of x varies through - 1, f’(x) does not changes its sign.

Then, x = - 1 is the point of inflexion.

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