Given the functionf(x)=2x³9x²over the interval1x6, answer the following questions.

(a)Findf(x)andf(x).

f(x)=

f(x)=

(b)Find the critical points off.

Enter the exact answers in increasing order.

x₁=

x₂=

(c)Find any inflection points off.

Enter the exact answer.

x=

d)Evaluatef

at its critical points and at the endpoints of the given interval. Identify local and global maxima and minima off

in the interval.

Enter the exact answers and then choose from multiple choice.

f(x₁)=__________

a.a global maximum b.a local minimum c.a global minimum d.a local maximum.

f(x₂)=__________

a.a global minimum b.a local maximum c.a local minimum d.a global maximum.

f(1)=__________

a.a global minimum b.a local maximum c.a local minimum d.a global maximum.

f(6)=-__________

a.a global maximum b.a local maximum c.a global minimum d.a local minimum.