What are the approximate values of the minimum and maximum points of f(x) = x5 − 10x3 + 9x on [-3,3]? a. maximum point: (–2.4, 37.014) and minimum point: (2.4, –37.014) b. maximum point: (2.4, –37.014) and minimum point: (–2.4, 37.014) c. maximum point: (–1.4, 33.014) and minimum point: (1.4, –33.014) d. maximum point: (–3, 30) and minimum point: (3, –30)

(-2.4, 37.014)

Step-by-step explanation:

We are not told how to approach this problem.  

One way would be to graph f(x) = x^5 − 10x^3 + 9x on [-3,3] and then to estimate the max and min of this function on this interval visually.  A good graph done on a graphing calculator would be sufficient info for this estimation.  My graph, on my TI83 calculator, shows that the relative minimum value of f(x) on this interval is between x=2 and x=3 and is approx. -37; the relative maximum value is between x= -3 and x = -2 and is approx. +37.  

Thus, we choose Answer A as closest approx. values of the min and max points on [-3,3].  In Answer A, the max is at (-2.4, 37.014) and the min at (2.4, -37.014.

Optional:  Another approach would be to use calculus:  we'd differentiate f(x) = x^5 − 10x^3 + 9x, set the resulting derivative = to 0 and solve the resulting equation for x.  There would be four x-values, which we'd call "critical values."

A. Maximum point :(-2.4,37.014)

Minimum point: (2.4,-37.014).

Step-by-step explanation:

Given function

f(x)= on interval

A. Maximum point (-2.4,37.014)

Minimum point (2.4,-37.014)

f(x)=

f(x)=-79.62624+138.24-21.6

f(x)=37.014

Put x= 2.4 then we get

f(x)=

f(x)=79.62624-138.24+21.6

f(x)=37.014

B. Maximum point (2.4,-37.014)

Minimum point (-2.4,37.014)

Put x= 2.4. Then we get

f(x)= -37.014

Put x=-2.4 then we get

f(x)= 37.014

C. Maximum point ( -1.4, 33.014)

Minimum point ( 1.4, -33.014)

Put x=-1.4 then we get

f(x)=

f(x)=-38.94

Put x= 1.4 then we get

f(x)= 38.94

D. Maximum point ( -3,30)

Minimum point ( 3,-30)

Put x=3 then we get

f(x)= 243-270+27=0

Put x=-3 then we get

f(x)= -243+270-27=0

Hence , from option A,B,C and D we can see only option A is right answer.

The approximate values of the minimum point (2.4,-37.014) and maximum  point (-2.4, 37.014) of the function f(x)= on .

55

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