I need help with my Calculus class, please explain in detail and thank you so mu

Question

I need help with my Calculus class, please explain in detail and thank you so much.

(Please Print) SHOW ALL RELEVANT WO (25 points and 3 pages) ORK IS LOGICAL BOXx LOGICL WOK BE SURE ALL ANSWERS ARE SIMPLIFIED AND THAT ALL | YOUR ANS L10] (1) Consider the function given by fx Find f(x) in FACTORED FORM YOUR ANSWER NO CALCULATOR!! constant. ction given by f(x) =-x3 + 3ax-2a, where a > 0 and a) Just for fun, , her sketch of the functi Find the set of critical numbers of f ; and, count the number of elements in A, find n(A). and, count the number of elements in A,find n() c) Make a sign chart for f"(x). c) Make a sign chart for f(x)

Explanation / Answer

if y = u.v, then

y' = u'.v + v'.u

2.

f(x) = (cos x)^3*sin 3x

f'(x) = 3*(cos x)^2*(-sin x)*sin 3x + (cos x)^3*(cos 3x)*3

f'(x) = 3*(cos x)^2*[cos x*cos 3x - sin x*sin 3x]

we know that

cos (a + b) = cos a*cos b - sin a*sin b

Using above relation

f'(x) = 3*(cos x)^2*cos (x + 3x)

f'(x) = 3*(cos x)^2*cos 4x

f'(x) = 3*cos2x*cos 4x

B.

h(x) = x^3*(3x - 1)^2

h'(x) = 3x^2*(3x - 1)^2 + x^3*2*(3x - 1)*(3*1 - 0)

h'(x) = 3*x^2*(3x - 1)*[3x - 1 + 2x]

h'(x) = 3x^2*(3x - 1)*(5x - 1)

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