If S1 and S2 are respectively the sets of local minimum and local maximum points of the fu…

Question

If S1 and S2 are respectively the sets of local
minimum and local maximum points of the function,

f(x) = 9x4 + 12x3 -- 36x2 + 25, x $$ \in $$ R,
then :

Accepted Answer

f(x) = 9x4 + 12x3 -- 36x2 + 25

f'(x) = 36x3 + 36x2 -- 72x

f'(x) = 36x(x2 + x -- 2)

f'(x) = 36x(x + 2)(x - 1)

While moving
left to right on x-axis whenever derivative changes sign from
negative to positive, we get local minima, and
whenever derivative changes sign from positive
to negative, we get local maxima.

$$ \therefore $$ S1 = {--2, 1}

S2 = {0}

Solutions · 1